Two balls, with masses \(m_{1}\) and \(m_{2}\), both moving along the same straight line, strike one another head-on in a one-dimensional elastic collision.

(a) Show that the magnitude of the relative velocity between the two balls is the same before and after the collision.

(b) Also show that if a video were made of such a collision, and then shown to an audience, the viewers could not be sure from the motion of the balls whether the video were being run forward or backward in time. That is, such collisions are said to be timereversal invariant.

(c) Would this time-reversal invariance still be true if the collision were inelastic? Give an example.