Suppose you hold a small ball in contact with, and directly over, the center of a huge ball if you then drop the small hall 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 and the small ball has velocity . (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?
Solution 98P Step 1 of 3: Let a be the large ball and B be the small ball and +y be the upward direction. so v B1y = v and v A1y =+ v Mass is inversely proportional to speed so If the large mass has much greater mass than the small ball its speed is changed very little in the collision and v =+ v A2y Step 2 of 3: a) vB2y vA2y = ( v B1y - v A1y) v = v v + v B2y A2y By A1y = v (v ) + v = 3 v After the collision the small ball moves upward with 3v speed.