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```					  Physics   Unit: 2

Physics – Unit 2
Unit 2
Why would a swimmer crossing a river end up some
distance downstream?
Pacing: 4 Weeks
Report Period 1

Key Concepts/Overarching Questions
KEY CONCEPT                       OVERARCHING QUESTIONS
Key 1:                                           1. What is the acceleration caused by gravity?
Free fall occurs at approximately the same       2. Does the speed of a falling object always
acceleration anywhere on Earth.                  increase?

Key 2:                                           1. What are vectors?
The simultaneous motions of an object in two     2. What is the process for adding vectors?
perpendicular directions occur independently     3. How does trigonometry assist in finding the
from each other.                                    sum of vectors?
4. What controls a projectile’s time in the air?

It is recommended that one day per unit is spent on reviewing PSSA open-ended type questions.
Physics   Unit: 2

Unit 2 Overview

Alignment to Standards

Focus Pennsylvania Standards
3.4.12.C Apply the principles of motion and force.
3.4.10.C Distinguish among the principles of force and motion.
3.1.12.B Apply concepts of models as a method to predict and understand science and
technology.
3.2.12.B Evaluate experimental information for appropriateness and adherence to relevant
science processes.
3.2.12.C Apply the elements of scientific inquiry to solve multi-step problems.

Eligible Content
S11.C.3.1.3 Explain that acceleration is the rate at which the velocity of an object is changing.
S11.C.3.1.2 Design or evaluate simple technological or natural systems that incorporate the
principles of force and motion.
S11.A.1.1.2 Analyze and explain how to verify the accuracy of scientific facts, principles,
theories, and laws.
S11.A.2.1.5 Communicate results of investigations using multiple representations.
S11.A.3.3.3 Analyze physical patterns of motion to make predictions or draw conclusions.
Physics   Unit: 2

Unit 2 Overview

Unit Texts                     Additional Resources                  Supplies & Materials
TEXT AND ASSOCIATED                   ADDITIONAL                          SUPPLIES AND
RESOURCES                       RESOURCES                           MATERIALS
 Holt Physics                   Holt Physics One Stop Planner         Whiteboards and
supplies
 Holt Physics Study Guide Book  Conceptual Physics-2009               Accelerometer
   Metal Washers
 Holt Physics Test Book         Lab Sheet-Acceleration of a           String
falling object.(at the end of       Coins- 2 per lab group
 Holt Physics Problem Book         this unit)                          Plastic Jar with air tight
lid
 Lab Sheet – Accelerated               Fishing Bobber
Motion Table. .–Blank and           Meter Sticks
Completed                           Notebook Paper
 (at the end of this unit)             Protractors
   Stopwatches
   Calculator or computer,
Photogates and
interfaces
   Pendulum support
   Pendulum masses
Physics    Unit: 2

Unit 2 at a Glance
Pacing: 4 weeks

Module         Pacing               Key                  Overarching Questions           Student Products

Free fall occurs at    1.What is the acceleration            Completed Study
approximately the same   caused by gravity?                   Sheet
acceleration anywhere  2. Does the speed of a falling        Solved Problems
on Earth.                 object always increase?            Velocity vs. Time
1              9 days
graph
 Evidence/data
recorded in notebook
 Exam
The simultaneous          1. What are vectors?               Completed Study
2              10         motions of an object in   2. What is the process for          Sheet
days       two perpendicular             adding vectors?                Solved Problems
directions occur          3. How does trigonometry           Completed
independently from           assist in finding the sum of     accelerated Motion
each other.                  vectors?                         Sheet
4. What controls a projectiles     Evidence/data
time in the air?                recorded in notebook
 Exam
Required Culminating Project: Throughout this unit the acceleration is given as g=9.8 m/sec2.
Use a pendulum and the equation (T = 2(l/g)1/2) to calculate the acceleration of gravity, g.

The students should generate a multiple paragraph summary based upon the evidence collected in their
notebooks that supplies the following items:
 Detailed algebraic solution of the period equation to produce g=42l)/ T2
 A drawing of the lab setup
 A data table of the pendulum’s periods and pendulum’s lengths
 Sample calculations, including units that show how the calculations were performed.
 An explanation of the process used to determine the final value of g

This will count as a multiple paragraph composition that is to be kept in the student portfolio stored in
the physics lab.

Suggested Unit Performance Assessment:
“Shoot the Monkey” Experiment: Explanation and Analysis

(See the materials at the end of the unit.)
One Dimensional Motion

Important Topics
Using Numbers to Describe Reality
 Recognize the importance of units when making measurements
 Know the standard units for measuring time (seconds, minutes, hours)
 Know how to convert units from one to another, given a conversion factor
 Recognize rates in multiple contexts – distance covered/time, water flow/time. Money
earned/time, etc.
 Use numbers written in scientific notation in their calculations
 Express numbers in scientific notation
 Know the SI units for measuring distance and describing position
 Know some of the basic conversion factors within the SI system and between the SI system and
the English system
Distance and Displacement
 Recognize the role of the sign (+/-) when describing 1-D motion
 Recognize that there are certain quantities that must have a direction to be fully described
Speed and Velocity
 Define speed as a particular rate – the rate at which position changes
 Know how to measure the speed of an object, using appropriate tools
 Know how to use the definition of average speed to calculate speed, distance covered or elapsed
time
Graphs of Motion
 Know how to make a graph of data
 Know how to interpret a position vs. time graph to find the location of an object at a particular
time
 Know how to interpret a position vs. time graph to find the time at which an object reaches a
particular location
 Know how to correctly interpret the slope of a line on a data graph, including the proper units for
the slope
 Recognize the correlation between the slope of a line on a position vs. time graph and the speed
of an object
 Be able to describe the motion of an object based on the shape (linear or curved) of the position
vs. time graph
 Differentiate between instantaneous and average velocity
 Recognize that the position vs. time relationship for an accelerating object is different than that
for an object with unchanging velocity
 Know the shape of a position vs. time graph for an accelerating object

Differentiation for PSP
 Correlate the shape of a graph with the mathematical equation of the relationship
 Know the relationships between d, v and a graphs in terms of slopes and areas under curves
Acceleration
 Recognize objects that have a changing velocity
 Define acceleration
 Define initial velocity
 Define final velocity
 Be able to use the definition of acceleration in order to determine the acceleration, initial
velocity, final velocity, or time elapsed for an object in motion
 Be able to recognize the motion of objects that have accelerations that are in the same or in the
opposite direction as their velocity
 Know the relationships between acceleration, displacement, initial and final velocity and time
for uniformly accelerating objects when the initial velocity is zero

Differentiation for PSP
 Know the relationships between acceleration, displacement, initial and final velocity and time
for uniformly accelerating objects with non-zero initial or final velocities (not including
problems requiring the use of the quadratic formula)
Freefall
 Know that gravity causes objects to accelerate
 Know that gravity must be a consideration for any object near the surface of the earth
 Know the magnitude and direction of the acceleration due to gravity near the surface of the earth
 Know the definition of freefall
 Know the conventions used by physics textbooks when describing freely falling objects (no air
resistance, uniform gravitational field, level plain, no earth spin, etc.)
 Define g

Key Terms
   Metric System                      Significant figures               Displacement
   SI                                 Graphical relationships           Time interval
   Base unit                          Linear relationships              Distance
   Meters                             Inverse relationships             Average velocity
   Seconds                            Quadratic relationships           Average speed
   Kilograms                          Square root relationships         Instantaneous velocity
   Scientific notation                Coordinate system                 Average acceleration
   Factor label method                Origin                            Instantaneous
   Precision                          Vector                             acceleration
   Accuracy                           Scalar                            Reference frame
Formulas
x  vt                                         v2  vi2  2ax
f

v f  vi                                            x rise
a                                             slope      
t                                               y run
v  at                                         Differentiation for PSP
1 2
x     at                                                1
2                                         x  vi t  at 2
2

 v  vf                                               1
x i           t                             x  v f t  at 2
 2                                                    2

Threshold Problems
Conceptual problems         Computational problems               Differentiation for PSP
 Holt p.68 #1-6             Holt p.28 #11b, d, g                Holt p.69 #11
 Holt p.69 #12-15           Holt p.59 #5                        Holt p.71 #37, 40
 Holt p.70 #26-29           Holt p.44 #5, 6
 Holt p.70 #21, 23, 30
 Holt p.881 #44
 Holt p.64 #2b
Two Dimensional Motion

Important Topics
Graphical Vectors
 Know the definition of vectors, scalars
 Utilize vector arrows to represent vector quantities
 Know the conventions for defining directions for vectors (degrees away from +x axis, cardinal
compass points, compass directions)
 Construct vector scale drawings with a ruler and protractor
 Know that a negative vector is the same a positive vector, with head and tail reversed
 Determine resultant vector graphically from multiple component vectors
Mathematical Solutions of Vectors
 Determine resultant magnitude of perpendicular vectors using Pythagorean theorem
 Adjust velocities in the presence of external vectors (i.e. river current, wind, etc.)

Differentiation for PSP
 Know how to resolve (decompose) vectors using trigonometric relationships
 Know how to use a scientific calculator to calculate trig relationships
 Determine angle of vector using inverse trig function (for right triangle only)
 Decompose multiple (non-axis) vectors and calculate resultant
 Decompose multiple non-orthogonal vectors and calculate resultant
Projectile Motion
 Explain that the horizontal motion of a projectile is constant velocity
 Understand that the vertical component of motion of a projectile is accelerating
 Combine the aspects of constant velocity in the x direction and accelerated motion in the y
direction to solve simple projectile problems when initial vertical velocity is zero
 Know the physics conventions for projectile motion problems (no air resistance, uniform
gravitational field, flat, level, infinite plane)
 Know the value of the acceleration and velocity for a projectile at critical points in a projectile’s
trajectory, including launch, peak, and impact (no calculations)

Differentiation for PSP
 Use equations of motion for projectiles to find any of the following: displacement (x, y, final),
velocity (x, y, initial, final), time, velocity vector angles, range when launched at an angle across
a level plain
Key Terms
   Angle                           Vector addition                Differentiation for PSP
   Degrees                         Resultant                          Theta
   Direction                       Coordinate system                  Hypotenuse
   Magnitude                       Horizontal                         Opposite side
   Vector tail                     Components                         Sine
   Vector body                     Trajectory                         Cosine
   Trigonometry                    Projectile                         Tangent
   Vector diagram                  Parabolic                          Inverse sine
 Inverse cosine
 Inverse tangent

Formulas
A B C
2       2     2                                Differentiation for PSP

Differentiation for PSP                                     OPP 
  sin 1     
 HYP 
OPP
sin θ 
  cos1       
 HYP 
cosθ 
HYP                                            OPP 
  tan 1      
tan θ 

Threshold Problems
Conceptual problems              Computational problems                Differentiation for PSP
 Holt p. 108 #1-20              Holt p. 109 #23, 25, 32,               Holt p. 110 #34
 Holt p. 109 #27-30               43a                                   Holt p. 881 #54
Physics   Unit: 2

Unit 2 Instructional Pathway

Module 1: SNAPSHOT
Free fall occurs at approximately the same
Pacing:2 weeks
acceleration anywhere on Earth.
Objectives: Students will be able to:
1. Explain the difference between speed and velocity.
2. Describe acceleration
3. Explain the meaning of the area under a velocity vs. time plot
4. Explain the significance of the slope of a velocity vs. time plot.
5. Describe the effect of air friction on the speed of falling objects.
6. Solve accelerated motion problems.

CE’s & PE’s:
Students will know that…
CE 2-1-1: Displacement, velocity, and acceleration are vectors, while distance and speed are scalars.
(STANDARD 3.4.12.C) (ELIGIBLE CONTENT S11.C.3.1.3, S11.A.3.3.3)
CE 2-1-2: In uniformly accelerated motion, the velocity changes linearly with time, while the
displacement changes as a square of time. (STANDARDS 3.4.12.C, 3.2.12.C) (ELIGIBLE
CONTENT S11.C.3.1.3, S11.C.3.1.2, S11.A.3.3.3)
CE 2-1-3: Free-fall motion is uniformly accelerated; the motion of an object thrown vertically
upward is uniformly decelerated. (STANDARDS 3.4.12.C, 3.2.12.C) (ELIGIBLE CONTENT
S11.C.3.1.3, S11.C.3.1.2,S11.A.3.3.3)

Students will be able to…
PE 2-1-1: Apply the concepts of non-uniform motion to the qualitative and quantitative analysis of one-
dimensional motion, including solving equations and performing the dimensional analysis.
(STANDARDS 3.4.12.C. 3.2.12.C, 3.1.12.B)
PE 2-1-2: Use equations of uniformly accelerated motion to interpret experiments involving free fall.
(STANDARDS 3.4.12.C. 3.2.12.C, 3.1.12.B, 3.2.12.B)

Text References, Materials & Supplies:

Resource                                          Needed Supplies
Holt Physics, p. 38-65                             Whiteboards and supplies
Holt Physics Test Book p. 9-16                     Computer and Internet access, LCD and
Screen
Holt Physics, Study Guide p 7-12                   Acceleration of a Falling Object Lab Sheet
and Accelerated Motion Table-Blank and
completed (found at the end of the unit)
Holt Physics Problem Workbook p 9-16            Overhead Projector and Transparencies or
ELMO

Instructional Pathway:

1. Penny-Quarter Drop
2. Hewitt-Conceptual Physics Discover Activity on falling objects page 46.
3. Acceleration of a falling object – lab
4. Data analysis and accelerated motion equation development from lab
5. Accelerometer used to identify the occurrence of acceleration.
6. Completion of the Accelerated Motion Table
7. Discussion of average velocity and instantaneous velocity
8. Solution of accelerated motion problem.
9. Review
10. Exam
Assessments (formative and/or summative):
1. The one stop planner provides a test question bank that permits the teacher to build an exam
customized to the students in class.
2. The Holt Physics Test Book has both basic and advanced level exams prepared for this module
that are found on pages 9 – 16
Differentiation:
    Algebraic solution of two simultaneous equations to produce the third equation 2as = vf2 + vo2
    Calculation of the acceleration of the falling object from the slope of the velocity vs. time graph.
    Different approaches to the use of the Acceleration of a Falling Object Sheet.
Physics   Unit: 2

Module 1: DETAILED
INSTRUCTIONAL PATHWAY
ENGAGE                                                                                Teacher Notes:
Day1                                                                                  Differentiation / Scaffolding
Ask the students if they know what will happen if a penny and a quarter are           & Common Misconceptions
dropped from the same height at the same time.                                        Teachers Notes:
Flat sheets that are
Accept all answers and then ask one of the students to drop the penny and             not folded or wrinkled
quarter. Both will contact the floor at the same time.                                will float downward
along unpredictable
Now ask the students what will happen if two sheets of composition paper are          paths.
dropped from the same height at the same time.
Folding the paper, or
Accept all answers and then drop two sheets of paper so that the students can see     crumpling it into
the results. Ask the students to use their notebooks to record what they feel is      more compact shapes
causing the result different from the coins.                                          will expose less
surface area to the
Give the students the opportunity to share their reasons with each other and reach    surrounding air. The
some type of consensus.                                                               reduced area reduces
the air friction
Ask the students to share their answers along with evidence for the answers they      allowing it to increase
gave.                                                                                 its speed at a faster
rate and travel along
Divide the students into groups and ask them to determine what will happen if         a more predictable
they change the shape of the papers and then drop the papers. Ask them to write       path.
down a prediction and then redo the experiment with multiple different shapes.
Require them to use their notebooks to record their results.

At the conclusion of the class, ask each group to report their finding to the class
using the white boards. Ask the students to also indicate if their predictions held
true for different paper shapes.

Day 2
Perform the discover activity found on page 46 of the 2009 Conceptual Physics
Teacher Text.
Ask the students the following questions:
1. How do the time intervals between the washer impacts compare?
2. What would happen to the time intervals if the washers were evenly spaced?
3. What general statement can you make about the distance traveled by the
falling washers during each second of flight?
The students are expected to:                                                          Do not attempt to do
1. observe the demonstration.                                                          any calculations at
2. make a prediction about washers falling with equal spaces between them and          this time for the
3. test that prediction.                                                               Discover activity.
4. use the evidence from these two demonstrations to answer question 3.                Simply ask the
students to make
The students should record the answer for question 3 in their notebooks with the       general observations
evidence for that answer.                                                              and descriptions.

EXPLORE                                                                                Allow the students to
Day 3                                                                                  test their answers to
Assign the students to work in lab groups to perform the lab activity                  question 2 by trying
“Acceleration of a Falling Object” found at the end of this unit.                      the demonstration
with equal distances
Day 4                                                                                  between the washers.
Ask the students what the increased dot spacing tells them about the falling
mass?                                                                                  The purpose of this
lab is to show that
Ask the students how they would calculate the area of a rectangle and the area of      falling objects move
a triangle. Record their responses for everyone to see                                 faster as they fall and
then to develop the
EXPLAIN                                                                                equations of
Display a diagram of the students’ paper strip graph (diagram #3) in the               accelerated motion.
Acceleration of a Falling Object activity.

Teacher Note:
The time between dots
was determined to be

The five dot intervals
on the tapes will then
Draw a rectangle and a triangle on the graph as shown in the diagram below             be 0.10 seconds.

Explain that the area of the rectangle is the velocity in the original time interval   The time between the
times the time the object falls. (v0t) since v = s/t when this is rearranged we get    dots does NOT
s = vt (the area of the rectangle) (The area of this rectangle calculates the          change.
displacement of an object moving at a constant speed.) The vt is the first term is
the accelerated motion equation s = v0t + ½ at2                                        The increased
distance between the
The area of the triangle is ½ bh or ½ vt where the v is the height of the triangle.    dots indicates
The acceleration can be calculated by dividing the magnitude of the velocity           increasing speed for
change by the time change. a = (vf – v0/t. The area of this triangle is the “extra”   the falling mass. This
displacement of the falling mass because it increases its speed as it falls)           answers the
overarching question
We are measuring the time change from zero and the change in the velocity              for Module 1 “Does
magnitude from zero so we will write this acceleration equation as a = v/t.(the v0     the speed of a falling
object really
drops out)                                                                           increase?”.
Differentiation:
Rearranging this equation for v gives us v = at.                                     Developing the third
equation for
Substituting this into the area equation for a triangle (½ vt), we get the area of   accelerated motion
the triangle expressed as ½(at)t or 1/2at2.                                          requires extended use
of algebra to
Combining these two area equations gives us s = v0t + ½ at2                          simultaneously solve
This is the accelerated motion equation that allows us to calculate straight line    the first two
displacement during acceleration.                                                    accelerated motion
equations.
For the basic students
explain that the third
equation,
2as = vf2 + v02 is
obtained by solving
two simultaneous
equations. More
might work through
the solution either in
By rearranging the equation for the definition of acceleration a = (vf – v0)/t to    class with the
solve for vf we get the first accelerated motion equation, vf = v0 + at              instructor’s help or as
an exercise for
NOTE: See the differentiation notes for suggestions as to how to proceed from        homework.
this point.
Also, the more
DAY 5                                                                                will be able to
calculate the slope of
Ask the students to each write out in their own words, without using equations,      the velocity vs. time
the meaning of the term, acceleration.                                               graph in (cm/sec)/sec.
Depending upon their
They should respond with some form of the idea that acceleration is a change in      tape timer, they will
velocity.                                                                            get an acceleration of
approximately 600 to
Ask one student to walk in the classroom so that they accelerate. They will have     700 cm/sec2. Ask
three possible correct answers.                                                      them to explain why
1. Walk in a straight line with increasing speed. (change in speed)                  this is smaller than
2. Walk in a straight line with decreasing speed.(change in speed)                   the acceleration
3. Walk in a circle with a constant speed.(change in direction)                      caused by gravity.
Show the students how to use the accelerometers in the lab and then allow the        (980 cm/sec2.)
students to verify their answers with an accelerometer.
Student
As the students experiment with a jar accelerometer, they should find that the       Misconception
bobber leans in the direction that the walker is gaining speed.(Verification for     Students do not
answer #1) They should find the bobber also leans opposite to the direction of       always understand
motion as they lose speed.(Verification for answer #2)                               what acceleration
means. The activity
They should also find that the bobber will lean toward the student if the student      starting day 5 is
holds the jar at arms length and spins about an axis through their own body.           intended to help to
(Verification for answer #3)                                                           develop this
understanding
If you do not have an accelerometer of any type, the instructions for building a jar
accelerometer are below.

Make an accelerometer if the classroom does not have one.
If the classroom lacks an accelerometer, build one in a clear glass or plastic jar.
In addition to the jar, you will need approximately 30cm. of string and a spherical
plastic fishing bobber.

Cut a piece of string that is six to ten cm. longer than the diameter of the opening
of the jar.

Attach the bobber to the remaining string and cut the string to a length to allow
the bobber to reach 3/4 of the way to the bottom of the jar.

Attach the bobber string to the middle of the string that is six to ten centimeters
longer than the diameter of the jar’s opening.

Fill the jar so that the water level is slightly above the top of the jar. Place the
bobber and string assembly in the water. Hold the short string across the opening
of the jar while putting the lid on the jar. (trap both ends of the short string
between the jar and the lid.)

When the jar is closed and then placed on its lid, it should allow the bobber to
stand up in the middle of the jar without touching the sides.

When the jar is moving at a constant speed in a straight line and then decreases
its velocity, the water will continue to move forward and it will push the bobber
backward indicating a negative acceleration.

An increase in speed pushes the water backward and the bobber forward
indicating a positive acceleration.

Moving the accelerometer through a circle at a constant speed will push the water
to the outside of the circle and the bobber toward the center of the circle
indicating an acceleration that points toward the center of the circle.

The acceleration of the accelerometer above is toward the right.
ELABORATE
Day 6                                                                                   Teacher’s note
Sometimes the
At this point, many teachers review the three accelerated motion equations and          students do not
give the students a problem assignment. Before doing this, ask the students to          believe that the
explain the difference between average velocity and instantaneous velocity. Give        average of a string of
them a few minutes to discuss this in small groups and then ask each group to           numbers on the
explain the different velocities in their own terms, using their notebooks to justify   number line is the
their answers (Accountable Talk).                                                       sum of the first and
last integer divided by
Hand out the accelerated motion table.(The table is found at the end of the unit in     two.
two forms, completed and blank) The idea is that an object that falls without
friction in the earth’s gravitational field will accelerate at 9.8 m/sec2. For this     Demonstrate this by
activity, we are going to round this acceleration to 10 m/sec2 in order to eliminate    writing down the
the need for a calculator in the activity.                                              integers from 1 to 10.
The table asks the students to fill in the values for a falling object for the          up (55) and then
acceleration at the end of each second, the speed at the end of each second, the        divide that answer by
average speed during each second, the distance traveled during each second, and         the number of
finally the total distance traveled while accelerating.                                 integers (10) the
The acceleration is given as 10 m/sec2 and should be filled in as the acceleration
at time equals zero and the end of each second.                                         Then ask the students
The object is dropped from rest so the speed at time equals zero seconds equals         integer, 1 and the last
zero m/sec. Since the speed increases by 10 meters/sec. each second, the speed at       integer, 10. Divide
the end of the first second will be 10m/sec, 20 m/sec at the end of the second          the answer (11) by 2
second and 30 m/sec at the end of the third second. The students will quickly see       and the average is 5.5.
the pattern and recognize the connection between the speed at the end of each
second and the acceleration.                                                            Repeat this process
with different integer
The average speed during each second can sometimes cause the students some              strings until they feel
trying moments. The quickest way to get average speed during the second                 confident that the
second, is to add the speed at the beginning of the second second (this is also the     average can be
speed at the end of the first second) to the speed at the end of the second second      legitimately calculated
and then divide the sum by two. This gives (10m/sec + 20 m/sec)/2 = (30                 by adding the first
m/sec)/2 which simplifies to 15 m/sec as the average speed during the second            and last integers and
second.                                                                                 then dividing by 2.

To complete the distance traveled in each second column, ask the students what
distance a car will travel in one hour at an average speed of 60 miles per hour.        Differentiation:
some type either from the text or from their notebooks. The students eventually         motion sheet can be
will get around to 60 miles as the distance traveled. It may be surprising to find      approached in a
that all students do not immediately give the correct answer. Give the students a       number of ways
few minutes to work this out. Some believe it to be a “trick question”                  depending upon the
ability of the students.
object will fall in one second at an average speed of 5 m/sec. Extend this to each    might complete this as
average speed in sequence.                                                            an independent
assignment.
Finally ask the students to determine the total distance an object will fall from
rest at the end of each second. If they have problems with this explain that by the   PSP students might
end of the second second, the object falls 5 meters in the first second and 15        complete this as a lab
meters during the second second for a total distance of 20 meters fallen in two       activity with the
probing questions.
Ask the students to complete the column on total distance fallen at the end of
each second.                                                                          Mainstream students
may need a teacher
Ask the students how much work would be involved in constructing a table to           centered approach
determine the distance fallen by the object in 20 seconds.                            with the teacher
After listening to the students responses, remind them of the equation for            then using the
displacement (s = vot + ½ at2) that was developed in the falling mass lab activity.   answers to complete
Show them how to use it to calculate the distance fallen in two seconds and then      the sheet in class.
ask them to verify the total distances fallen at the end of each second.
All students should do
Most students will compare the accelerated motion table to the calculated values      this activity in some
and use this as evidence that the equation is valid and much less work.               form.

Ask the students to explain the source of the equation (s =vot + ½ at2). Give         For most students the
them time to use their notebooks to produce the evidence from the acceleration of     mention of the terms,
a falling object lab. Accept all their answers but guide them to use the evidence     differential calculus,
from the lab to explain that the area under the plot is calculated by the             or integral calculus is
displacement plot.(Accountable Talk).                                                 enough to turn them
off to what is being
taught in this class.
ELABORATE
Day 7                                                                                 Do not mention these
terms. Students who
Assign the students a number of problems from the Holt Physics textbook               later take calculus will
appropriate to their abilities. Accelerated motion problems can be found on           quickly make the
pages 53, 55and 58. Additional problems are found in the Holt Physics Problem         connection between
Workbook on pages 3 through 15.                                                       physics and calculus

Day 8
Review the materials on accelerated motion in preparation for an examination.
Review sheets can be found on pages 7-12 of the Holt Physics Study Guide

EVALUATE
Day 9
Two different levels of ready made exams on accelerated motion can be found
from page 9 through page 16 of the Holt Physics Chapter Tests Book. Additional
test questions can be found in the One Stop Planner CD.
Physics   Unit: 2

Unit 2 Instructional Pathway

Module 2: SNAPSHOT
The simultaneous motions of an object in
two perpendicular directions occur            Pacing: 2 weeks
independently from each other.
Objectives: Students will be able to:
1. Distinguish between a vector and a scalar.
2. Add and Subtract vectors using the graphical method.
3. Apply the Pythagorean theorem and trigonometry functions to calculate the magnitude and
direction of a resultant vector.
4. Resolve vectors into components using the sine and cosine functions.
5. Recognize examples of projectile motion
6. Describe the path of a projectile as a parabola

CE’s & PE’s:
Students will know that…
CE 2-2-1: Displacement, velocity, and acceleration are vectors, while distance, speed and time are
scalars. (STANDARD 3.4.12C) (ELIGIBLE CONTENT S11.A.3.3.3)
CE 2-2-2: Two-dimensional motion can be described by the two independent, simultaneous motions in
each of the dimensions. (STANDARD 3.4.12C) (ELIGIBLE CONTENT S11.A.3.3.3)
CE 2-2-3: Projectile motion consists of uniform horizontal motion and free fall, which occur
simultaneously. (STANDARD 3.4.12.C, 3.4.10.C) (ELIGIBLE CONTENT S11.C.3.1.3,
S11.A.3.3.3)

Students will be able to…
PE 2-2-1: Perform addition and subtraction of vectors. (STANDARDS 3.4.12.C., 3.2.12.C)
PE 2-2-2: Apply vector addition to solving multi-step problems involving one- and two-dimensional
motion. (STANDARDS 3.4.12.C., 3.2.12.C)
PE 2-2-3: Represent motion in two dimensions by a system of equations describing the independent
motion in each dimension separately. (STANDARDS 3.4.12.C., 3.2.12.C)
PE 2-2-4: Interpret evidence gathered from an experiment and solve multi-step problems involving
projectile motion. (STANDARDS 3.4.12.C., 3.2.12.C)

Text References, Materials & Supplies:
Resource                                     Needed Supplies
Holt Physics, p. 80-105                      Computer and Internet access, LCD and
Screen
One Stop Planner                             Two demonstration coins
Problem Workbook p. 19-20                    Meter Sticks
Study Guide p. 13                             string

Test Book p. 17-24                            Metal washers
Rulers and Protractors
Calculators

Instructional Pathway:
1. Two coin projectile demonstration.
2. Meter stick projectile model construction
5. Vectors to model projectile motion
6. Importance of both magnitude and direction in vector addition
7. Homework – study guide
8. Homework problem Workbook
9. Review
10. Exam
Assessments (formative and/or summative):
1. The one stop planner provides a test question bank that permits the teacher to build an exam
customized to the students in class.
2. The Holt Physics Test Book has both basic and advanced level exams prepared for this module
that are found on pages 17 – 24
Differentiation:
    Variation in the sequence of introduction of trigonometry functions
Physics   Unit: 2

Module 2: DETAILED
INSTRUCTIONAL PATHWAY
Day 1                                                                                 Teacher Notes:
ENGAGE                                                                                Differentiation / Scaffolding
Set up a coin so that it is sitting with half of its mass over the edge of a table.   & Common Misconceptions

Teacher Notes:
Ask the students to draw a diagram in their notebooks of what they expect will        The time to the floor
happen when the coin is struck by a coin of identical mass that is traveling on a     for the coin that
path that is toward the edge of the table and is perpendicular to the edge of the     moves sideways and
table.                                                                                the coin that drops
straight down will be
Give the students time to draw up the diagram and write out their expectations.       identical no matter
Allow them to discuss this with each other to come to a consensus.                    how high above the
floor the coin begins.
Ask the students to share their beliefs on what will happen. Determine if there is
a difference of opinion between groups and identify those differences.                The time to the floor
is determined by the
Once this is accomplished. Perform this demonstration. Do the demonstration a         beginning altitude.
number of times to allow the students to prove or disprove the students’
expectations.

EXPLORE
Ask the students to break into groups and perform this coin activity from
different heights above the floor. The students should record all observations and
conclusions in their notebooks.

The questions the students must answer are:
1. How does the time for the moving coin to fall to the floor compare to the time
for the coin at rest to fall to the floor?
2. Does the speed of the moving coin affect the time for the coin to fall to the
floor?
3. What determines the time for a coin to fall to the floor?

DAY 2
EXPLAIN
At the beginning of the class, ask the student groups to take few moments to meet
and review their findings from yesterday.

The student groups will report their findings to the class. The groups must use
their notes from the investigations to support the answers to the questions listed
above.

Ask the students to refer to the Acceleration of a Falling Mass activity. The
students should examine the total distance fallen at the end of each second.
The students working in groups should connect an individual string to a number
of metal washers and cut the strings so that when suspended from a meter stick,
they will hang below the edge of a meter stick by the following distances; 5 cm,
20 cm, 45 cm, 80cm, 125 cm., and 180 cm..(These distances are in the same ratio
as the total distance fallen in the activity.)                                        Teacher Notes:
The horizontal
Connect the washers suspended from the strings to a meter stick so that the           spacing of the strings
position of the washers mimic a stop action photo of the coin that moved              on the meter stick are
sideways off of the table top. Have the students answer the question: “What does      equal distances. This
the horizontal spacing of the washers tell you about the horizontal speed of a        indicates a constant
projectile.”                                                                          speed. When the
speed is given a
The meter stick should look like something like the diagram below.                    direction it becomes a
velocity vector.
The trajectory model demonstrates that no matter which direction the projectile is
launched (the direction of the meter stick) gravity will always make the projectile   The horizontal
fall the same distance below the launch direction in the same amount of time.         velocity is constant so
Have the students demonstrate how to use the model to mimic different launch          the strings are
angles and notice the only thing that changes is the shape of the parabola. The       attached at equal
distance below the meter stick does not change.                                       intervals. The
horizontal velocity is
caused by a horizontal
push that puts the
projectile in motion
and then stops
pushing. After the
push stops there is no
acceleration.

The vertical velocity is
caused by gravity that
continues to act
during the entire time
the object falls. As
demonstrated in the
Acceleration of the
Falling Mass
Experiment, the
distance fallen each
second continuously
increases.
The projectile model
is described on page
76 of Conceptual
Physics, 2009

At the conclusion of the class, ask the students to identify what they have learned.
Accept all answers but guide the students responses to include but not be limited
to the following:
1. A projectile has two motions-horizontal and vertical.
2. The motions are independent. (One accelerates-the other does not accelerate)
3. Speed with a direction is a vector (a number with a direction) known as
velocity.

Day 3
Engage
Ask the students to evaluate 2 + 2 and 3 + 3. in their notebooks.

The students will easily treat these number as scalars and generate the correct

Remind them that they have also studied numbers with directions: displacement,
velocity, and acceleration. Remind them that the displacement is the straight line
distance from the starting point.
Ask the student to add 3 and 4 as scalars. They will easily give the answer of 7.

Ask a volunteer to walk 3 floor tiles along the floor and then turn right and walk
4 tiles across the floor. Ask the student to find the magnitude of his or her
displacement (5) and the direction. Some may want a protractor and some may
simply point in the correct direction. The important point is that the students
should look for some way to describe direction.

Ask the class to draw an arrow in their notebooks that describes the 4 tile
distance the student first walked. Then draw an arrow connected to it that
describes the 3 tile distance. The students should not have too much trouble
drawing something like the diagram below.

Ask the students to draw the vector that represents the displacement. (The
straight line distance the student would have to walk to go from the starting point
to the ending point.)

resultant gets longer
and points more and
more in the
This will take some repetition for the students to develop an understanding.           downward direction.

Once the students get the idea that the vectors are added head to tail and the
resultant (displacement vector in this case) is drawn from the starting point to the
ending point, add vectors only at right angles to begin with and use the
Pythagorean Theorem to calculate the magnitude of the resultant vector.

The students should be able to do this with vectors drawn to a scaled length and
then, eventually, mathematically

Remind the students that the projectile is subjected to two independent motions.
A constant horizontal velocity and a varying vertical velocity. Picking two
velocities and adding them as vectors results in a resultant velocity.

On the board and in their notebooks, ask the students to add a longer vertical         Differentiation:
velocity to the fixed horizontal velocity. Do it several more times with a longer      Some students are
vertical velocity each time. See the diagram below.                                    ready to solve
problems of this type
with the trig functions
sine, cosine and
tangent. Introduce or
review these functions
as needed to meet the
needs of the students.
and 843 to 845 in Holt
Ask the students to check out each other’s work and describe what generally            Physics. And solve
happens to the resultant velocity when the vertical velocity continues to get larger   problems 1 to 4 page
because gravity is always pulling downward on the projectile                           92.

The exercise is also intended to help the students to realize that the horizontal      Assign the Vector
velocity doesn’t change and the vertical velocity does change.                         Operations Study
Guide found on page
Just as at the beginning of the day, ask the students to evaluate 2 + 2 and 3 + 3.     14 of the Holt Physics
They should do the work in their notebooks. But this time treat the numbers as         Study Guide Book
vectors.

Some of the students will automatically draw the vectors at right angles and
generate the answers of 2.8 = 2 + 2 and 4.2 = 3 + 3.

EXPLAIN
If this happens, point out that these are the correct magnitudes but ask them
which direction the original vectors should point.

In fact, no directions were given so there are a number of possible answers that
range from zero to four to nine and a number of answers in between.
Demonstrate how the vectors can be added to give these various answers.

Remind the students that a direction must always be given in order to get the
correct magnitude and direction.

For homework, assign the Introduction to Vectors study guide sheet found on
page 13 of the Holt Physics Study Guide Book.

DAY 4
EXPLAIN
Ask the students to assemble in their lab groups and determine if everyone in
their group can individually explain how they solved the problems assigned for
homework. Give the groups a few minutes to sort things out and then select a
representative from each group to solve a randomly selected problem from the
study guide in front of the class.

The students must not only provide the correct answer but also provide evidence
from their notes that the answers are correct.

Assign the students to read Holt Physics pages 86 to 94; and solve problems 1 to
4 on page 89.

EXPLAIN
DAY 5
Review the homework and have the students explain the reasons for their
methods.

Assign pages 17 and 18 in the Problem workbook as homework and allow the
students to begin the work in class.

DAY 6
Review the homework and have the students explain the reasons for their
methods.

Assign pages 19 and 20 in the Problem workbook as homework and allow the
students to begin the work in class.

DAY 7
Review the homework and have the students explain the reasons for their
methods.

Review the material in Module 2 for an exam.

Day 8
Exam
Physics   Unit: 2

Unit 2 CULMINATING PROJECT
Shoot the Monkey” Experiment                      Pacing: 1 day
“Shoot the Monkey” Experiment: Explanation and Analysis
Teacher’s Notes

The performance assessment should take one class period to complete, including the demonstration and/or
computer demonstration. It is designed to test the students’ grasp of two-dimensional motion and, ideally,
its mathematical description. The inquiry should result in applying the newly-acquired understanding of
projectile motion to a new context in which a projectile launched at an angle must hit a moving target.
Students should be given an opportunity to view the “Shoot the Monkey” experiment and/or view its
interactive computer demonstrations (see Supplemental Teacher Resources). No measurements are
necessary for this task. However, if computer workstations are available for the students to use, an
interactive virtual lab with controlled variables may be easily designed (see http://jersey.uoregon
.edu/vlab/newCannon/NewCannon_plugin.html). You can provide students with a choice for their virtual
lab inquiry: vary the initial speed or vary the launching angle to find how these changes influence hitting
the target. Students may work in groups of 4–6, depending on the availability of the computer
workstations. The group may work on the explanations and analysis together, but each student should
produce an individual written account of the inquiry and its conclusions. The pacing of the investigation
allows time to review the concepts of projectile motion and time for students to ask questions as the
assignment is introduced. The scoring rubric (p. CG-70) is meant to be shared with students.
The students should perform as much hands-on work as possible. Make sure to spend extra
time discussing the physical meaning of the demonstrations. Let them satisfy their curiosity by
experimenting with the interactive software. Explain to the students that many physicists work this way
very successfully. Tell them about Michael Faraday, a physicist who changed our civilization though he
detested math. Those students who have already studied projectile motion at an angle should have no
difficulty deriving formulae to support their explanation of the experiment or performing the analysis of the
experimental situation. These students should use trigonometry, linear and quadratic equations, and can be
allowed to perform an independent inquiry, formulating their own questions and seeking answers.
The Relative Speed
Scoring Rubric
Discuss the following rubric with students so they know what is expected of them:
Score Explanations Analysis
4 Explanation of both scenarios is completely clear and accurate. The descriptions of the experimental
evidence are presented and interpreted correctly. The qualitative reasoning involves all steps. Schematic
drawings for both scenarios are accurate and correctly labeled. All vectors are correctly identified and their
components resolved. Excellent communication skills are used in all written work. The analysis for both
scenarios correctly represents the physical reality of the situations and includes the conditions inherent in
the scenarios. Includes the outcome of the experiment in the absence of gravity. All the equations are
derived correctly. The chart of equations is completely filled out and accurate for both scenarios. The
comparison between the free fall of the “monkey” and the launching of the projectile is complete and
includes quantitative reasoning.
3 Explanation of at least one scenario is clear and completely accurate. Description of the experimental
evidence is presented and interpreted correctly. The qualitative reasoning and schematic drawings are
mostly accurate and correctly labeled. Most vectors are correctly identified and their components resolved.
Good communication skills are used in all written work. The analysis for at least one scenario correctly
represents the physical reality of the situations but does not include all the conditions inherent in the
scenarios. Includes the outcome of the experiment in the absence of gravity. Most equations are derived
correctly. The chart of equations is completely filled out but contains a few minor errors. The comparison
between the free fall of the “monkey” and launching of the projectile is complete but does not include
quantitative reasoning.
2 Explanation of both scenarios has some errors.     The description of experimental evidence for one of the
scenarios is presented and interpreted correctly. The qualitative reasoning involves all steps. Schematic
drawings are present but contain multiple errors. Some vectors are correctly identified and their components
resolved. Good communication skills are used in all written work. The analysis of both scenarios has some
errors and does not correctly represent the physical reality of the situations, nor does it include the
conditions inherent in the scenarios. The role of gravity is poorly defined or not included. Some equations
are derived correctly, and the chart of equations is partially filled out. There is no comparison between the
free fall of the “monkey” and launching of the projectile.
1 Major pieces of the assessment are missing or incomplete. Evidence and reasoning are presented poorly
and filled with inaccuracies. Poor communication skills are displayed in written work. Major pieces of the
assessment are missing or incomplete. The quantitative reasoning is missing or incomplete. The analysis is
based on unrealistic and inaccurate reasoning.
Name ________________________________________________________ Date __________

“Shoot the Monkey” Experiment: Explanation and Analysis
Observe the “Shoot the Monkey” experiment and/or interactive computer demonstrations and
explain what you observe quantitatively.
The Shoot the Monkey demonstration is one of the experimental proofs of the principle of independence of
motions. It may be shown in a variety of ways, but the idea is the same: you are shooting at an object (the
monkey) which is simultaneously released from rest. Use your knowledge of projectile motion and free fall
to describe the experimental evidence, explain the observed phenomena, and analyze various conditions
that make the scenario possible, impossible, or different.

1. Explain why the monkey will almost always be shot.
2. Make a schematic drawing, with the height of the monkey H and its horizontal distance from the gun L
clearly shown. Connect the gun and the monkey by a straight line. What does this line represent?
3. On the same drawing, show the initial velocity V0 of the bullet. Remember the gun is pointed directly at
the monkey.
4. Resolve the vector into the horizontal and vertical components, V0x and V0y. The basic triangle and the
triangle of velocities are similar, which means: V0y /V0x = H/L Note: this will be helpful for your analysis.
5. Figure out what happens to both the bullet and the monkey and finish the equations of their motion in the
chart below. Fill in the appropriate information wherever there is a “?” present. Remember that the motion
of the same object in x- and y-directions occur simultaneously and independently from each other. The
bullet and monkey meet (or hit) at x = L and time t = tmeet, at which point the bullet and monkey must be at
the same height, h. The bullet is a projectile that must travel to the point with coordinates (L, h) during the
time t meet. The monkey falls from rest, starting from the height H, to reach the height h at the time t meet;
it is already located at x = L (see your sketch). One-dimensional motion bullet (projectile motion) monkey
(free fall) x-direction L = V0x # ? Not applicable y-direction
h = ? # t meet - ? t2 meet/2 h = ? - gt2 meet/2
6. Formulate your explanation of the reasons why the bullet hits the monkey, based on the equations from
the chart above and from the similarity of the triangles: V0y = (V0xH)/L
Be sure to compare the free fall of the monkey with the launching of the bullet.
7. Try to formulate the conditions under which the bullet would not hit the monkey. Write a detailed
account of your inquiry, including the description of experimental evidence, verbal explanation and
analysis, and, finally, the mathematical reasoning that supports your conclusions.
NAME______________________________________________________ Period ___________

: Without using a calculator, fill in the blanks in this sheet for a falling object that accelerates at
10m/sec2.

Time         Acceleration     Speed at the       Avg. Speed         Distance         Total distance
(sec)         (m/sec2)         end of the        during the         traveled           traveled.
second            second.          during each            (m)
(m/sec)           (m/sec)            second.
(m.)
0
1
2
3
4
5
6
7
8
9
10
NAME______________________________________________________ Period ___________

: Without using a calculator, fill in the blanks in this sheet for a falling object that accelerates at
10m/sec2.

Time         Acceleration     Speed at the       Avg. Speed         Distance         Total distance
(sec)         (m/sec2)         end of the        during the         traveled           traveled.
second            second.          during each            (m)
(m/sec)           (m/sec)            second.
(m.)
0                10                0                  0                 0                 0
1                10               10                  5                 5                 5
2                10               20                 15                15                20
3                10               30                 25                25                45
4                10               40                 35                35                80
5                10               50                 45                45                125
6                10               60                 55                55                180
7                10               70                 65                65                245
8                10               80                 75                75                320
9                10               90                 85                85                405
10               10               100                95                95                500

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