AP PHYSICS C UNIT 2 PRACTICE TEST NAME_________________________________

FREE RESPONSE PROBLEMS

Show your work for partial credit. Circle or box your answers. Include the correct units and 3

significant figures in your answers! Use the back of the test if you need more space, and

clearly label each problem you put on the back.

1. The position of a particle is given by 𝑟 = (𝐴 sin(𝜔𝑡) 𝑖̂ + 𝐴 cos(𝜔𝑡) 𝑗̂) m, where 𝑡 is in seconds

and angles are in radians. (a) If the particle’s starting position is 4.5𝑗,̂ and the particle’s

starting velocity is 10.8𝑖̂, find the magnitude and direction of the particle’s instantaneous

acceleration at 𝑡 = 5.00 s. (b) Find the particle’s average acceleration from 𝑡 = 0.00 s to

𝑡 = 5.00 s. (c) Find the particle’s trajectory.

2. Jane Fisycks is standing on a second floor balcony, 2.25 m above ground, with a water

balloon. Her brother Joe is on the ground, running away from the building with a velocity

of 2.42 m/s in the positive 𝑥 direction. Jane throws the water balloon 10.8 m/s at an angle

of 35.0º above the horizontal. The water balloon hits Joe. Use the base of the building as

your origin. (a) How high does the balloon go into the air? (b) What is the magnitude

and direction of the water balloon’s velocity when it hits Joe? (c) Where was Joe when

Jane threw the water balloon?

3. Two pulleys are connected by a belt, as shown

at right. Point A is on the rim of the left pulley,

23.4 cm from its center. Point B is on the rim of

the right pulley, 36.8 cm from its center. When

two pulleys are connected by a belt, the

translational speed of the belt is the same

everywhere on the belt. The left pulley has a

constant rotational speed of 14.6 rad/s. (a) Find the period, frequency, and rotational

speed of the right pulley. (b) Find the magnitude and direction of the acceleration at

Points A and B. (c) Find the translational speed of the belt.

A B

4. A boat whose speed in still water is 4.20 m/s heads across a river 4.64 km wide, pointing

upstream at an angle of 65.0º west of north. The current is a constant 4.0 m/s south. (a)

Find the velocity (magnitude and direction) of the boat relative to the shore. (b) How

many minutes does the trip to the other side require? (c) What speed would the boat

need (relative to the water) to travel directly across the river perpendicular to the

shoreline?