Question

In a game of pool, the cue ball moves at a speed of 2m/s toward the eight ball. When the cue ball hits the eight ball, the cue ball bounces off with a speed of 0.8 m/s at an angle of 20 degrees, as shown in the diagram below. Both balls have a mass of 0.6 kg.

a) What is the momentum of the system before the collision? (Write it in component form)
b) What is the momentum of the system after the collision?
c) Write the velocity of the cue ball after the collision in component form.
d) What is the x-component of the velocity of the eight ball after the collision?
e) What is the y-component of the velocity of the eight ball after the collision?
f) At what angle does the eight ball travel after the collision?
g) What is the magnitude of the eight balls' velocity after the collision?

Answer 1

a) The momentum of the system before the collision is (1.2 kg m/s, 0).

b) The momentum of the system after the collision is (0.96 kg m/s, 1.44 kg m/s).

c) The velocity of the cue ball after the collision is (0.64 m/s, 1.28 m/s).

d) The x-component of the velocity of the eight ball after the collision is 0.64 m/s.

e) The y-component of the velocity of the eight ball after the collision is 1.28 m/s.

f) The eight ball travels at an angle of 63.4 degrees after the collision.

g) The magnitude of the eight balls' velocity after the collision is 1.6 m/s.