A steel ball-bearing drops onto a smooth hard surface from a height h. The time to the first impact is T = √(2h/g) where g is the acceleration due to gravity. The times between successive bounces are 2eT, 2e²T, 2e³T, . . . , where e is the coefficient of restitution between the ball and the surface (0 < e < 1). Find the total time taken up to the fifth bounce. If T = 1 and e = 0.1, show in a diagram the times taken up to the first, second, third, fourth and fifth bounces and estimate how long the total motion lasts.