Question

A rubber ball of mass m is dropped from a height h. If the ball loses energy on each bounce so that its speed just after each bounce is 90% of its speed just before each bounce, then Önd an expression for the height the ball reaches after the 3rd bounce

Answer 1

Let speed before any bounce be Vo
speed after bounce is 0.9Vo
Kinetic energy before any bounce = Ko
Kinetic energy after bounce = (0.9)² Ko = 0.81 Ko
kinetic energy before first bounce = mgh (initial potential energy of ball is converted to kinetic energy just before bounce)
Kinetic energy after 3rd bounce = (0.81)³ mgh
                                                   = 0.53 mgh
Height after 3rd bounce = 0.53h