A ball is thrown horizontally from a height h above a staircase as shown in the figure. If the coefficient of restitution for any collision between the ball and the staircase is e , then the value of h for which the ball will bounce the same height above each step, is

Step-by-step solution

Vertical velocity of the ball just before each collision is v app = 2 g h The height up to which the ball bounces after each collision is h ' = h - d Vertical velocity of the ball just after the collision is v sep = e v app = e 2 g h Using the principle of conservation of mechanical energy we get 1 2 m e 2 g h 2 = m g h - d 1 2 e 2 2 g h = g h - d e 2 h = h - d d = h 1 - e 2 h = d 1 - e 2