Suppose you hold a small ball in contact with, and directly over, the center of a large ball. If you then drop the small ball a short time after dropping the large ball, the small ball rebounds with surprising speed. To show the extreme case, ignore air resistance and suppose the large ball makes an elastic collision with the floor and then rebounds to make an elastic collision with the still-descending small ball. Just before the collision between the two balls, the large ball is moving upward with velocity V and the small ball has velocity -v. (Do you see why?) Assume the large ball has a much greater mass than the small ball.
(a) What is the velocity of the small ball immediately after its collision with the large ball?
(b) From the answer to part (a), what is the ratio of the small ball's rebound distance to the distance it fell before the collision?