Motion in Two Dimensions
1. Two baseballs are pitched horizontally from the same height but at different speeds. The faster ball
crosses home plate within the strike zone, but the slower one is below the batter’s knees. Why does the
faster ball not fall as far as the slower one? After all, they travel the same distance and accelerate down
at the same rate.
2. A Teflon hockey puck slides without friction across a table at constant velocity. When it reaches the
end of the table, it flies off and lands on the ground.
a. Draw the situation above, drawing vectors showing the forces on the puck at two positions while
it is on the table and at two more when it is in the air. Draw all vectors to scale.
b. On a separate diagram, draw vectors showing the acceleration on the puck in the same four
locations.
c. On a separate diagram, draw vectors showing the horizontal and vertical components of the
puck’s velocity at the same four locations.
d. Using a different color pen or pencil, draw the total velocity vector at the same four points
3. Suppose an object is thrown with the same initial velocity and direction on the moon, where g is 1/6 as
large as on the Earth. Will the following quantities change? If so, will they become larger or smaller?
A) vx and vy B) Time of flight C) Maximum height D) Range
4. A stone is thrown horizontally at 8 m/s from a cliff 78.4 m high.
a. What is the initially vertical speed of the stone?
b. What is the vertical acceleration of the stone?
c. Upon landing, what is the stone’s vertical displacement?
d. How long did the stone stay in the air?
e. What is the horizontal velocity of the stone?
f. How far from the base of the cliff will the stone land?
5.
Janet jumps off a high diving platform with a horizontal velocity of 2.8 m/s and lands in the water 2.6
seconds later. How far away from the base of the platform does she land?
6.
A stone is launched at an angle of 25o from the ground with a velocity of 8 m/s. How far away from the
launcher does it land?
7. A batter hits a pitched ball at a 45o angle. It just clears the outfield fence, 98 m away. Assume the fence
is the same height at the pitch. What was the ball’s velocity as it went over the fence? (assuming no air
resistance)
8. A toy car runs off the edge of the table that is 1.225 m high. If the car lands 0.400 m from the base of
the table, how long does it take the car to fall and what is the horizontal velocity of the car.
9. An arrow is shot at a 30o angle with the horizontal. It has a velocity of 49 m/s. How high will the arrow
go? What horizontal distance will it travel?
10. A basketball player tries to make a half court jump shot, releasing the ball at the height of the basket.
Assuming the ball is launched at 51o, 14.0 m from the basket, what velocity must the player give the ball
11. A baseball is hit at 40 m/s at an angle of 53o with the horizontal. Immediately an outfielder runs 4 m/s
toward the infield and catches the ball at the same height it was hit. What was the original distance
between the batter and the outfielder?
12. A 3 kg weight is being twirled on the end of a 1.5 m rope. The weight makes two complete revolutions
every 7 seconds.
a. What is the period of the motion?
b. What is the frequency of the motion?
c. What is the velocity of the weight as it is twirled?
d. What is the centripetal acceleration of the weight?
e. What centripetal force is required to keep the weight in horizontal circular motion?
13. A little girl is swinging her new purse in a 1.5 m diameter circle over her head. The 200 g purse makes
5 revolutions every 2 seconds.
a. What is the period of the motion?
b. What is the frequency of the motion?
c. What is the velocity of the purse as it is circling overhead?
d. What is the centripetal acceleration of the purse?
e. What is the tension in the purse strap?
14. A merry go round exerts a force of 1000 N on a rider on the outer ring of animals when it takes 15
seconds to make a complete revolution. If the person weighs 750 N, what is the radius of the circle he is
making?
15. A toy airplane is attached to a string and is flying in circles near the ceiling of a store. The speed of the
plane is measured to be 2 m/s when the plane makes 2 revolutions every 7 seconds. What is the radius
of the circle the plane is making?
16. A record player is able to exert a force of 25 N on a 100 g record that has a diameter of 8 cm. What is
the speed of a particle at the edge of the record?
17. A record player makes 45 revolutions per minute. What is its period?
18. An object is being accelerated at 15 m/s2 when it is running in a 1.5 m circle. What is the velocity of the
object?
19. The posted speed for a 150 m radius curve is 45 mph (24.6 m/s). If you drive a 544 kg car, what is the
minimum amount of friction that must be exerted on your car to keep it on the road?
20. A toy plane is circling at 2.62 m/s in a 1.5 m circle. What is the frequency of the motion?
21. An object is being accelerated at 250 m/s2 as it moves around a 3 m diameter circle. What is the object’s
frequency?