A ball falls from a height H onto a fixed horizontal plane. The coefficient of restitution is e and the height reached by the ball in the nth rebound is H,. (a) Show that H, = e2" H (n = 1,2,...). (1) (b) If the ball travels a total distance D before coming to rest after a time T, deduce that D = = 1+e? 1+e /2H T = (2) H and 1- e2 - e (Neglect air resistance and any variation in g.)

A ball falls from a height H onto a fixed horizontal plane. The coefficient of restitution is e and the height reached by the ball in the nth rebound is H,. (a) Show that H, = e2" H (n = 1,2,...). (1) (b) If the ball travels a total distance D before coming to rest after a time T, deduce that D = = 1+e? 1+e /2H T = (2) H and 1- e2 - e (Neglect air resistance and any variation in g.)