A billiards cue ball moves towards two stationary balls that

Last updated: 7/31/2022

A billiards cue ball moves towards two stationary balls that are next to each other (one in front of the other). All the balls just move in a single direction, with the cue ball initially moving in the +x direction. Assume any collision between the balls conserves momentum. Each ball has a mass of 0.17 kg. The cue ball's initial velocity is +20 m/s and the other two balls are sitting still. After the cue ball hits the first still ball, the first still ball hits the second still ball immediately. The result is after the collisions, the cue ball moves backwards, -2 m/s in the x-direction. The first still ball (in the middle), moves forward in the x-direction with velocity +9 m/s in the x-direction. To conserve momentum, what will the velocity of the second (initially) still ball be? Show whether the kinetic energies of the balls are conserved in this set of collisions or not (consider the three balls as one system). If energy is gained or lost by the balls, calculate how much. If kinetic energy was lost, where might the energy have gone? Give at least 2 possibilities.