# Projectile Motion Projectile Motion Motion 1 Galileo

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```					                                                 Projectile Motion
Motion:
1. Galileo stated that every object has a resistance to change its state of motion called
______________. The more massive the object, the greater its inertia.
2. In the early 1500’s Copernicus stated that the earth was in a constant state of
motion. (People reasoned that this could not be true for if you jumped in the air
the earth would simply move underneath your feet and you would land elsewhere). See
section 4.9 pg. 55 Read “The moving Earth” pg. 36-37 (Flipping a coin in the car or a bird chasing a
worm from a tree).
3. Accelerations of objects occur due to net _________ acting upon them in the direction
of their motion. Any force acting perpendicular to the motion of an object will not cause
an acceleration of the object.
Projectiles (read pg. 33-36: pg. 184):
A cannonball shot from a cannon, a stone thrown into the air or a ball rolling off of a table are all
examples of projectiles.
a. Projectiles near the earth follow a curved or parabolic path.
b. Horizontally a projectile travels with a ___________ velocity (much like a ball rolling on a
frictionless table). This is an example of Newton’s _____ law, which states that an
object will continue in its state of rest or motion in a straight line path at a constant velocity unless
compelled to change the state of motion by some external force acting upon the object.
c. Vertically a projectile will accelerate at ________ m/s2 (as if it were dropped from rest).
d. When a projectile is fired upward at some angle, the original velocity will have
horizontal and vertical components (as in vector components). Treat these independently
(_______________ velocity horizontally and an acceleration of _______ m/s2 vertically).
See figure 3.11 and 3.12 pg. 36: 10.9 and 10.10 pg. 189
e. A projectile will reach its maximum horizontal displacement at an angle
of _______. See figure 3.13 pg. 36: 10.11 pg. 189.
f. Upward and downward velocities will have the ______ magnitude but opposite signs at the same
height. Fig. 3.16 pg. 37: 10.14 pg. 191.
Homework:
1. What is Newton’s First Law?
2. What is inertia?
3. What reasoning was used to discredit Copernicus’ idea that the earth was in constant
motion?
4. What is the cause of acceleration of objects?
5. When a ball rolls along a smooth horizontal surface, what can be said of its speed?
6. If you are sitting in your car traveling on a level surface at a constant velocity of
a. How fast is the book traveling relative to the road?
b. How fast is the book traveling relative to you?
c. If you were to drop the book and the car suddenly speed up, where would the book
land in relation to you?
7a. What can be said of a projectile’s horizontal velocity?
b. What can be said of a projectile’s velocity in the vertical direction?
c. At what angle should a projectile be thrown to achieve maximum horizontal displacement?
8a. If a ball is dropped from 4.9m , how much time will be required for the ball to hit the
ground?
b. if a ball is thrown horizontally from a height of 4.9 m, how much time will be required for the
ball to strike the ground.
c. If the ball in 8b. strikes the ground 20.0 m away from where it was thrown, what was the
horizontal velocity of the ball while it was in the air?
Projectile Problems
1. A projectile thrown parallel to the ground (horizontally) will fall at the _________ rate as it
would if dropped from rest.
2. The projectile will travel horizontally with a _____________ speed (velocity), neglecting air
resistance.
3. The projectile will ______________ vertically at a rate of 9.80 m/s2.
4. Horizontal and vertical motions are _______________ of each other.
5. For a projectile at equivalent vertical displacements upward or downward, the time to travel
upward will be __________ to the downward time, the magnitude of the initial upward velocity
will be _______ to the downward velocity but _________ sign (this will not be for different
vertical displacements).
6. A projectile dropped from a moving vehicle will have the same ______________ velocity as the
moving vehicle (neglecting air resistance).

Equations:
_
v = d/t = (vf + vo) / 2           a = (vf – vo) / t        d = ½ at2 + vot        vf2 - vo2 = 2ad

Sample Problem #1:
A B-29 bomber bomb from a height of 9450. m. If the bomb had a horizontal velocity of 67.0 m/s when it
was dropped, how far horizontally would the bomb have traveled when it exploded 513 m above the
ground?

Sample Problem #2:
A person is fired at a 40.0 º angle to the horizontal, with an initial velocity of 24.0 m/s from a canon at the
circus. He falls into a net that is at the same height as the mouth of the canon.
a. What will be the person’s vertical displacement at the highest point?

b. What would be the person’s horizontal displacement?
c. If the person falls into a net that is 5.0 m above the mouth of the canon (while traveling back down),
what would be the person’s horizontal displacement?

Homework
Day #1:
1.    While traveling 10.0 m/s, a ball rolls off of a table that is 2.5 m high. Calculate the horizontal displacement
of the ball. (like example #1)
2. Wiley Coyote runs off of a cliff and lands 10.0 m from the base of the cliff that is 35.0 m tall. Determine
Wiley’s horizontal velocity as he ran off of the cliff.
3. A projectile is fired upward 10.0 m/s at a 30.0º angle to the horizontal and returns to the ground at the same
height that
it left.(like examples 2a and 2b).
a. Determine the total horizontal displacement and
b. Determine the vertical displacement to the highest point.
4. A shot-putter throws a shot-put with an initial speed of 14.0 m/s at a 40.0º angle to the horizontal. The shot-
put leaves the shot-putter’s hand at a height of 2.20 m above the ground. Determine the horizontal
displacement of the shot-put (dy = 2.20 m). (like example 2c)
5. A hunter aims directly at the bottom of a target located 220.0 m away horizontally. If the bullet leaves the
gun traveling 550. m/s. Determine how far below the target will the bullet fall.
6. An Olympic long jumper is capable of jumping a horizontal distance of 8.00 m while taking off with a
horizontal speed of 9.0 m/s. (vo = -vf which means that the vertical displacement is 0 m)
a. How much time is the long jumper in the air?
b. How far does the jumper fall from his maximum height during his jump? (use ½ the time from 6a)
Day #2:
1.    A ball rolls off of a table with a horizontal velocity of 1.5 m/s and lands in a cup located 0.63 m from the
bottom edge of the table. Calculate the height of the table.
2.    George Blanda (once the NFL’s all time leading scorer) kicks a football with an initial velocity of 22.0 m/s
at an angle of 45.0º to the horizontal. Determine the maximum vertical displacement and total horizontal
displacements of the ball.
3.    Bob Beaman (an Olympic Gold medal long jumper) makes a horizontal leap of 9.00 m, while leaping at an
angle for 1.14 seconds. Determine the unknown angle. (remember that velocity vectors are composed of
velocity components so determine vx and voy)
4.    An ice cream container is dropped from an airplane to the Castaways of Gilligan’s Island from an altitude
of 455 m and traveled a horizontal distance of 355 m. Determine the plane’s velocity when it dropped the
ice cream if it was traveling parallel to the ground at the time of the drop.
5.    Mac Wilkins (an Olympic Gold Medal shot-putter) is running down the track at 7.85 m/s. While running,
at this pace he drops his shot put, which falls 1.50 m to the ground. Determine the horizontal displacement
of the shot put.
6.    Franz Klammer (the Olympic Gold medal skier) swooshes down a slope and hits a bump. He hits a bump
and travels upward at an angle of 15º to the horizontal at 15.0 m/s. He later lands back on the slope, 7.50 m
below where he left the slope. Determine Franz’s horizontal displacement during his leap from the slope.
Day #3:
1. Dick Weber rolls a bowling ball off of a 500.0 m tower with a horizontal velocity of 10.5 m/s. How far
from the base of the building does the ball land?
2. A person runs off of a cliff at 3.60 m/s and strikes the water below 2.00 seconds later.
a. How high was the cliff            b. How far from the base of the cliff does the person land?
3. Superman is said to be able to leap tall buildings in a single bound. How tall of a building could
Superman leap if he leaves the ground at 60.0 m/s at an angle of 75.0º to the horizontal?
4. An airplane will be dropping supplies to flood victims on a clearing of an island from an altitude of
300.0 m. The plane is traveling at a constant 155 km/hr.
a. At what horizontal distance must the supplies be dropped before the plane reaches the clearing?
b. How many seconds before the plane reaches the clearing must the supplies be dropped?
5. A toy rocket is fired at 15.5 m/s at a 35.0 o angle to the horizontal. The rocket returns to the ground at
the same height that it left the ground. Neglecting air resistance:
a. Determine the horizontal displacement of the rocket.
b. Determine the maximum vertical displacement of the rocket.
6. As shown in the figure below, a ball is thrown from the top of one building toward a tall building 50.0 m
away. The initial velocity of the ball is 20.0 m/s at an angle of 40.0º to the horizontal. How far below the
original level will the ball strike the opposite wall? (like example 2c).

20.0 m/s

40.0o

50.0 m

Bonus: A long jumper travels 8.90 m horizontally after leaving the ground at a 30.0º angle. What was the takeoff
speed at the 30.0º angle ?

Day #4:
1. George (of Presidential fame) climbed into his father’s cherry tree to fetch a basket full of cherries. Before
climbing the tree, George placed a basket on the ground, a horizontal distance of 2.5 m from the base of the
tree. When George was in the tree he threw cherries into the basket from a height of 3.2 m above the
ground. Determine the horizontal velocity that George threw the cherries to have them land in the basket.
(Of course, when the branch supporting George broke, in his anger, George chopped down the cherry tree).
2. Cy Young (MLB’s all time leader in wins) kicks his baseball horizontally from a cliff at 40.0 m/s. The ball
lands 50.0 m from the base of the cliff. Determine how far the ball fell.
3. Investigators of a car wreck notice that a car slid off of a small bridge in Madison County and landed in a
snow pile 4.00 m below the level of the road. The car traveled 12.0 m horizontally after leaving the road. How
fast was the car traveling when it left the road?
4. A person throws a dart with a speed of 15.0 m/s horizontally at the top of a 5.00 cm-wide bulls-eye of a dart
board from a distance of 2.20 m from the board. Will the dart hit or fall below the bulls-eye if it is on line?
5. Doodle Chaffins is jumping over a puddle 1.50 m long. He leaps from the edge of the puddle to a height of
0.200 m with the horizontal component of the velocity being 3.00 m/s.
a. What is Doodle’s horizontal displacement? (Does the person clear the puddle?)
Hint: To find the total time that Doodle is in the air, consider the time it takes to fall from the top of his
trajectory back to the ground and multiply this time by 2.
b. What was Doodle’s initial and final vertical velocities?
c. What was the magnitude and angle of Doodle’s initial jump velocity?
6. Basketball Jones (not of Celtic fame but of Cheech and Chong fame) shoots a ball with an initial velocity of
17.1 m/s at an angle of 40.0º to the horizontal from a height of 2.00 m above the ground. On its downward
descent the ball strikes the rim 3.05 m above the ground.
Determine the horizontal displacement of the ball. (dy = -1.05 m)

Bonus:
Jan Stenarud kicks a football at a 45º angle to the horizontal and it strikes a crossbar on its downward descent
10. feet above the ground and 55 yards from the point where it was kicked. Determine the initial velocity of the
kicked ball.
Free Fall and Projectile Lab
Always show blank equations, proper units on all values, and carry and underline at least one extra significant digit
from a calculation used in a calculation later, show the value with extra digits in the show calculation section.
Do not report any extra digits in the spaces provided on the sides.
Free Fall (Determining Reaction Time)
1. Have your partner hold a piece of paper above your fingers.
2. Try to catch the piece of paper when after it has been dropped by your partner. Measure how this distance
to the nearest 0.001 m and record in meters.
_________ m
3. Determine your reaction time using the distance from step 2
(show calculation below)

Projectile Lab                                                                                     _________ s
1. Place a Physics text books in a stack on your desk. Open the cover of the book in a manner such that it
makes a ramp whose edge rests exactly 2 cm from the edge of the desk.
2. Measure the height of the desk in meters to the nearest 0.001 m (100 cm = m)               _________ m
3. Place a ball bearing on the ramp, exactly 20 cm from the edge of the ramp. At the same time, place a meter
stick on the floor in line with the ball and edge of your desk (at the 0.00 m mark).
4. Allow the ball to roll down the ramp and record the distance where the ball strikes the meter stick from the
bottom of the desk (to the nearest 0.001 m).
__________ m

5.   Utilizing the horizontal distance (step #4) and height of the desk (step #2), determine the horizontal velocity
of the ball. (show calculation below, use x and y columns)

__________ m/s

6.   Measure the height of the lab bench in meters to nearest 0.001 m.                      __________ m
7.   Allow the ball to roll down the ramp from the same 20 cm mark used in part 4. Record how far the ball
travels horizontally from the bottom of the lab bench (to nearest 0.001 m)
__________ m

8.   From the height of the lab bench (step #6) and the horizontal velocity (step #5), determine the theoretical
distance the ball should travel (show calculation below, use x and y columns)

__________ m
9.   Determine the % error for steps #7 and #8. (use the value from Step #8 as the theoretical value)
(Show calculation below)

__________ %
Projectile Motion Interactive Lab Simulation
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/applet.html
Step #1
Set initial velocity to 50.0 m/s, angle to 90.0 o, mass to 10.0 kg              Max Height (m)           Total Time (s)
Perform on computer simulation and record values in table.

Determine max vertical displacement of the projectile
(Show calculation below. Don’t use computer time value from table, it is to

Vertical displacement ______________ m
Determine total time for the projectile to remain in the air.
(Show calculation below. Don’t use computer values from table, they are to be used to check your answer)

time   ______________ s
Step #2
Set initial velocity to 100.0 m/s, set angle to 30.0 o, and mass to 10.0 kg
Perform on computer simulation and record values in table

Determine the maximum vertical and horizontal displacement.                          Max Vertical      Max Horizontal
(Show calculation below. Don’t use computer time values, it is to be used            displacement      displacement

vertical displacement   ____________ m

horizontal displacement ____________ m

What other angle can be used to obtain the same horizontal displacement under the same conditions in Step #2?
Angle = ________

Step #3
Try different angle until you find the angle of maximum horizontal displacement. (Perform simulation to check
Angle = ________
Step #4
Hit the refresh button to clear the screen.
Enter the following conditions:
Velocity = 75.0 m/s
Angle = 45.0o
Mass = 100.0 kg

Record values in the table.
Trial             Mass          Max Displacement       Max Height         End Velocity         Total Time

1             100.0 kg

2             10.0 kg

3
click air        100.0 kg
resistance box
4
click air         10.0 kg
resistance box
What is the effect of mass on the maximum horizontal displacement of a projectile when air resistance is neglected? (be
sure to include the terms mass and air resistance in your answer)

What can you conclude about the effect of mass on the maximum displacement of a projectile when air resistance is
not neglected? (be sure to include the terms mass and air resistance in your answer)

Step #5
Find http://library.thinkquest.org/2779/Balloon.html

Assume the balloon falls a vertical distance of 50. m when it strikes the man below. Make sure you record your data
(velocity and angle) before you launch a balloon! Determine the horizontal distance the guy is from the base of the
building by changing the velocity and angle when you strike him with a balloon. DO NOT change the gravity or
wind.

Angle _______ o (measured to the one’s place)                 dy = 50. m

velocity = __________ m/s (measured to the one’s place)               dx = ____________ m
(show calculation below)

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