# Kinematics Problems Velocity by nikeborome

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```									    AP Physics B
Summer Assignment
2008

Have a great summer!
Dr. Basu
OBJECTIVE:

The purpose of this assignment is to reinforce the Physics concepts you learned last year.

PROCEDURE:

- You will review thoroughly the following Physics topics:

I. KINEMATICS
II. NEWTON'S LAWS
III. WORK, POWER AND ENERGY
IV. MOMENTUM AND COLLISIONS
V. CIRCULAR MOTION

-   All the information needed to answer the questions and solve the problems in the
packet is in the Holt Physics Textbook.
-   Also consult the PHYSICS CLASSROOM website. You will be able to review basic
physics concepts through these tutorials. They have very nice animations and
explanations especially geared toward high school students. Each tutorial has additional
problems for you to practice and attain mastery over the material
-   You MUST attempt ALL questions and problems. If there is a particular problem that
you cannot complete, be sure to show all your work for the problem.

-   Draw neat free-body diagrams and other diagrams wherever necessary.

DATE DUE:
-This assignment is due on the second day of school, and will be graded either as a Quiz
or Test.

EXTRA HELP:
You may email me at rbasu@monroe.k12.nj.us if you have any questions or need help with
the assignment.

DISCLAIMER: The Master Schedule for 2008-2009 will not be in place until summer.
This assignment is being handed out to all students who have requested AP Physics in
2008-09. Receiving this assignment in no way guarantees or indicates that you will be
placed in the AP Physics class in 2008-09. Do not begin to work on this packet until
July 15th, at which time the master schedule should be set, and you should know of
Kinematics Problems-Velocity

1) At a recent regatta in Texas, The San Antonio Crew Classic, results from the Men's Tex-Visitors Cup
Grand Final with their times are as follows:

The course is 2000m long. Assuming constant velocity for all boats, how far behind OSU was each boat when
OSU crossed the finish line? (UCSD=39m, Columbia=45m, UCI=53m, WSU=68m, UCSB=74m)

2) At a track meet at Hayman Field, a runner does one quarter-mile lap in 1.25 minutes. Assuming she starts
and stops at the same point:

a. What was her average speed during this lap? (5.4m/s)
b. What was her average velocity for this lap? ( 0 m/s)

3) A train is moving towards a destroyed bridge. The velocity of the train remains constant at 20m/s. A person
inside the train realizes that they will die unless they run to the back of the train and jump out. If the person is
15m from the back of the train and the back of the train is 50m from the break in the track, what velocity must
the person run with to make it to the back of the train just as the back of the train goes over the break in the
bridge...
a. relative to the train? (-6.0m/s)
b. relative to the ground? (14 m/s)

4) Train A starts at 4 km South of a bridge and heads North at a constant speed of 30 km per hour. Train B
starts 6 km North of the bridge.

a. What velocity must Train B have so that the two trains cross the bridge at the same time? (-45.1 Km/h)
b. If Train B goes at 35 miles per hour, South, how far away from the bridge do they cross? (.62 km N of bridge)

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1D Kinematics-Constant Acceleration

1) You are asked to do an experiment to measure g. You set up a device which drops a metal ball from rest
from a height of 1.650m. Using an accurate timing device which detects the release of the ball and its landing
on the floor, you measure the average time of the falling ball to be 0.585s.
a. What do you measure the value of g as? (-9.64m/s2)
b. Can you give an explanation as to the error from the accepted value of 9.8 meters per square second?

2) A car starts from rest and travels for 10 seconds with a constant acceleration of 3.0 m/s2 The driver then
applies the brakes causing a constant negative acceleration of -4.0 m/s2. Assuming the brakes are applied for
2.0 seconds:
a. How fast is the car going at the end of braking? (22 m/s)
b. How far has the car gone at the end of braking? (202 m)

3) A ball is thrown straight up in the air and passes a certain window 0.30s after being released. It passes the
same window on its way back down 1.50s later. What was the initial velocity of the ball?(10.3 m/s)

4) A model rocket is launched from rest and its engine delivers a constant acceleration of 8.2 meters per
square second for 5.0s after which the fuel is used up. Assuming the rocket was launched straight up into the
air and assuming no air resistance
a. Find the maximum altitude reached by the rocket. (188m)
b. Find the total time the rocket is in flight. (15.4 s)

5) A jogger with a constant velocity of 4.0 meters/second runs by a stationary dog. After 1 second, the dog
decides to chase the jogger. The dog accelerates at 1.5m/s2.
a. How long does it take the dog to catch the jogger? (6.19 s)
b. How far away from the spot where the dog was sitting has the jogger gone when she is caught by the dog?
(28.7m)
Note: Assume the jogger is listening to walkman and doesn't realize the dog chasing her until it's too late. In
other words assume constant velocity for the jogger.

6) A water balloon is dropped from rest from the top of a 20.0m cliff. At the same time, a person at the bottom
of the cliff shoots an arrow up towards the water balloon. The arrow strikes the water balloon after 0.300
seconds.
a. How far up the cliff does the arrow strike the water balloon? (19.56 m)
b. What was the arrow's initial velocity? (66.7m/s)

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Two-dimensional Kinematics (Projectiles, etc.)

1) Caught between the Jay Walker foot bridge and the Purposeless bridge, a good swimmer needs to cross the
Bubbling Brook river as fast as possible. His speed swimming is 1.50 meters per second. The current of the
river is 1.00 meters per second and the river is 15 meters wide.

a. How long will it take him to swim across the river if he takes account of the current and swims so that his
body remains at the same lateral position in the river while crossing it(ie. he travels exactly perpendicular to
the bank), ending up on the far bank exactly across from where he started. (13.4 s)

b. If instead he lets his body be carried downstream by the current while just aiming his body for the other
bank and swimming, how long will it take to get across the river, and how far downstream from his point of
starting will he end up? (10 m)

2) You have a machine that launches a brick at a speed vi, θ0 above the horizontal. You can use this device to
measure the height of a building.

a. Given and the distance d that the brick lands from the building, find an equation for the height h of the
building in terms of vi, θ0 and d. ( h= ½g[ d/vi cosθ]- dtanθ)
b. You use this machine set at initial speed 10 m/s and θ=30 degrees. You find that the brick lands 18m away
from the base of a building. How high is it? (10.8 m)

3) The farthest a person can throw a ball with no air resistance (         ) is s.
a. If they threw the ball with the same initial speed, but straight up, how high would it go as a fraction of
s?(s/2)
b. If the max distance were 60.0m, what would be the max height? (30.0m)

4) A football is thrown to a moving football player. The football leaves the quarterback's hands 1.5m above
the ground with a speed of 15 m/s at an angle 25 degrees above the horizontal. If the receiver starts 10m away
from the quarterback along the line of flight of the ball when it is thrown, what constant velocity must he have
to get to the ball at the instant it is 1.5m above the ground? (5.8 m/s)

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5) A plane with supplies is at an altitude h a distance over ground x from its drop point and the nose makes an
angle θ below the horizontal.

a. What speed must the plane have at that moment to be able to release its supplies and have them land right
on the drop zone? (√gx2/2cos2θ(h – xtanθ)       )
b. When does this equation blow up (what are the limits of the variables)? Why? (h >= xtanθ)
Ignore air resistance and consider θ to be the direction of the velocity of the plane.

6) Two cannons, one aimed 450(left) from horizontal, the other aimed 600 (right) from horizontal, are
simultaneously fired toward each other .

a. In order for the two projectiles to collide, at some point in time the y components of position must be the
same. Since the cannons were fired simultaneously, show that this means the y components of their initial
velocities must also be equal.
b. Given what you showed in part a, and that projectiles are fired from the left cannon at 100 m/s, determine
the required initial velocity of projectiles fired out of the right cannon for an impact to occur. (81.6 m)
c. If the cannons are 1.3 km apart, when does this impact take place? (11.6 sec)
d. Where does it take place? (Give x,y coordinates relative to the left-hand cannon) (x=820.2m, y=160.9m)

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Newton’s Laws & Friction Problems

1) Let a force act on a mass m1. A mass m2 is added and you observe that the acceleration dropped to of its
former level. Assuming the force remained the same, find the ratio of m1 to m2.

2) The maximum (or terminal) velocity of a skydiver (m=70kg) with arms and legs extended is about 120
mi/h (= 53.6 m/s).

a. What force does air resistance exert on the skydiver? (686 N)
b. If the skydiver pulls in their arms and aims their body downward, the terminal velocity can be increased to
about 180 mi/h (= 80.5 m/s). What force does air resistance now exert on the skydiver? (686 N)

3) At takeoff, the combined actions of engines and wings on a plane produce a force of 90,000 N at an angle
of 600 above the horizontal. The plane rises at a constant velocity in the vertical direction while continuing to
accelerate in the horizontal direction. (HINT: In the vertical direction there is no acceleration, which means
no net force. The weight of the plane balances the vertical component of the lift exactly. a) 7953 Kg & b)
5.66m/s2)

a. What is the mass of the plane?
b. What is the horizontal acceleration?

4) A 200 Newton block is suspended by 3 cables, as in the figure above. Find the tension in each cable.
(148.4 N, 79.0 N, 200N)

5) Masses 1 and 2 are connected by massless rope 1 going over a massless, frictionless pulley.
Mass 2 rests on a frictionless plane with an incline θ.

a. If rope 2 is attached to the ground, what is the tension in both ropes? { T1 = m1g , T2 = ( m1 - m2sinθ)g }
b. For what values of m1, m2 and θ are these equations valid?

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Newton’s Laws & Friction Problems (Contd.)

6) Find the normal forces acting on the sphere at points A and B. The mass of the sphere is 10.0kg.
(FA=56.6N , FB= 113N )

7) Fluffy dice of mass m hang from the rear view mirror of a car. Find the acceleration of the car (constant)
given the angle the massless cord makes with the vertical. (Hint: What forces act on the dice to make them
move? Given an angle theta, the dice move with the same acceleration as the car. ) (a = gtanθ)

8) The coefficient of static friction between your hand and a pie plate is about (0.8). If you want to put a
cream pie in someone's face, what minimum acceleration do you need to keep it from sliding down your
vertical hand? (Hint: There must be no motion in the y direction. ) (12.3m/s2)

9) The coefficient of kinetic friction between the block and the ramp is (0.20). The pulley is frictionless.
a. What is the acceleration of the system? (4.12 m/s2)
b. What is the Tension in the rope? (114 N)

10) What is the expression for the the acceleration of the blocks ''a'' and tension in the string ''T''? Assume:
1. m2>m1
2. System is in motion to the right
3. Coefficient of kinetic friction equal for both blocks (μ)
b. Show that the expression for acceleration obtained in part a. reduces to the proper equation if m1 = 0!

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Collisions

1) A 1.0kg block (a) moving at a speed of 4.0 meters per second runs head on into a 0.5kg block (b) at rest in
a perfectly elastic collision. What are the velocities of the blocks after the collision? (vaf =1.3m/s , vbf = 5.3
m/s)

2) A 10g bullet is fired horizontally into a 300g wooden block initially at rest on a horizontal surface and
becomes embedded in it. The coefficient of friction between block and surface is (0.50). The combined
system slides 4.0m before stopping. With what speed did the bullet strike the block? (194 m/s)

3) To measure the speed of a bullet, the following situation is set up. A wooden block (m=0.50kg) is put on
top of a fencepost with a height of 1.5m. The bullet (m=.010kg) strikes the block from a perfectly horizontal
direction and remains embedded in it. The block is measured to fall 1.6m from the base of the post. How fast
was the bullet going? (147 m/s)

Holt Pg. 235 Problems: # 47 (4.0×102) # 50 (.14m), # 51 (340 m/s), # 52 (2.36×10-2 m/s)

Work, Power and Energy

1) A tourist drags his suitcase (Weight 130N) a distance of 250m at a constant speed to catch his flight. He
exerts 60N at an angle 40 degrees above the horizontal.

a. What work does he do? (11.5kJ)
b. What work is done by friction?( -11.5kJ)
c. Find the coefficient of kinetic friction μk. (. .503)

2) A person pushes a stalled 2000 kg car from rest to a speed vf, doing 4000 J of work in the process. During
this time the car moves 20 m. Neglecting friction between the car and the road, find:

a. the final speed vf of the car. (2.0 m/s)
b. the horizontal force exerted on the car. (200 N )

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Work, Power and Energy (Contd)
3) You are driving home at 136 km per hour from a spring break vacation in British Columbia, when you see
a speed trap 100 meters ahead of you. Knowing that you'll get caught if you apply the brakes, you decide to
coast and pray you slow down in time. Nevertheless, you get stopped, and a grinning mounty informs you that
you were traveling at 110 kilometers per hour.

a. What was the force of friction on your 907kg car? ( 2320 N )
b. Assuming the speed limit was 100 kilometers per hour, what would have been the minimum force needed
to keep you from getting caught? (3040 N)

4) An elevator m=800kg has a maximum load of 8 people or 600kg. The elevator goes up 10 stories = 30m at
a constant speed of 4m/s. What is the average power output of the elevator motor if the elevator is fully loaded
with its maximum weight? (neglect friction) (54.9 kW)

5) A block is given an initial speed v0 up a ramp with an incline θ. The coefficient of kinetic friction between
block and ramp is μ.

a. In terms of v0, μ, θ find how far up the ramp the block goes d. .

b. Given an initial velocity of 3.0 meters per second, μ=0.50, and θ=25 degrees, find d. (0.52m)

6) A block (m=5.0kg) is released from point A and it slides down the incline ( = 30 degrees) where the
coefficient of kinetic friction is 0.3 It goes 5.0m and hits an ideal spring with a spring constant k=500
Newtons per meter. While it is being acted upon by the spring, assume it is on a frictionless surface.

a. How far does the block go up the plane on the rebound from the spring? (1.58m)
b. How far is the spring compressed? (.536m)

.

7) A small object of mass m slides without friction around the loop-the-loop apparatus shown in the figure. It
starts from rest at a height h above the bottom of the loop.
a. What is the minimum value of h (in terms of R) such that the object moves around the loop without falling
off the top (point B). ( h= 5R/2) ( Hint: think of the centripetal force at the top)

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Circular Motion
1) A car motor rotates at 800 revolutions per minute (rpm) in idle. When shut off, it accelerates at -20 radians
per second squared.
a. What is its angular velocity after 1.0s? (63.8 rad/s)
b. How long will it take for the motor to completely stop? (4.19 s)

2) Following a fiery explosion, a car tire, radius 0.4m, becomes separated from the car. It hits the ground and
without bouncing or slipping begins to roll in a straight line. Just after hitting the ground it has an angular
velocity of 18 radians per second. It rolls 35m before coming to rest upright. What was its average angular

3) A child on the outside edge of a carousel, diameter 8.0m, accelerates from rest to a final angular velocity of
2 revolutions per minute in 10.0s. Assume constant angular acceleration.

a. What is the tangential acceleration on the child during the 10s? (0.084 m/s2)
b. Find the magnitude of the child's total acceleration (centripetal and tangential) at 5.0s. (0.095 m/s2)

Holt Physics Pg: 272-3 # 48 (12 m/s), # 51(8.3s), # 53(0.131)

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