A ball is dropped from a height H onto a horizontal floor. During the collision with the floor, the ball loses 75 % of its kinetic energy. The coefficient of restitution between the ball and the floor, and the maximum height it reaches after the first bounce, respectively, are :

Step-by-step solution

Let the initial kinetic energy just before the collision be K_i = mgH . Since the ball loses 75 % of its kinetic energy during the collision, the kinetic energy retained just after the collision is K_f = 25 % of K_i = 0.25 mgH . The maximum height h reached after the bounce is determined by the retained kinetic energy: mgh = K_f = 0.25 mgH h = H 4 The coefficient of restitution e is the ratio of the speed of separation to the speed of approach: e = v_f v_i = K_f K_i = 0.25 = 0.5 Thus, the coefficient of restitution