Question

In a game of pool, a cue ball strikes an eight ball head on. Before the collision the cue ball is moving in the +x direction at 20 m/s while the eight ball is at rest. After the collision, the cue ball is at rest while the eight ball is moving in the +x direction with a speed of 20 m/s. Both the cue ball and the eight ball have the same mass. Which of the following statements is true?

A) The collision is elastic because linear momentum is conserved.

B) The collision is inelastic because the two objects are rigid and do not compress or
stretch.

C) The collision is elastic because kinetic energy is conserved.

D) The collision is inelastic because one of the objects is stationary after the collision.

E) None of the above statements is true.

Answer 1

In an elastic collision between a cue ball and an eight ball, statement A is true: the collision is elastic because linear momentum is conserved.

Step-by-step explanation:

The collision described in the question is an elastic collision. In an elastic collision, both momentum and kinetic energy are conserved.

In this case, the cue ball strikes the eight ball head on, transferring all of its momentum to the eight ball. As a result, the cue ball comes to rest and the eight ball moves with the same speed as the cue ball initially had.

Since both momentum and kinetic energy are conserved, statement A is true: The collision is elastic because linear momentum is conserved.