A ball is dropped on to a horizontal plate from a height h = 9 m above it. If the coefficient of restitution is e = 1 2 , the total distance travelled before the ball comes to rest is

Step-by-step solution

The impact between the ball and the plate is direct impact. If u is the velocity of the ball before impact, its velocity after is eu, where e is the coefficient of restitution. But u ⁡ = 2 gh since the ball falls from a height h. So the velocity of the ball at the first rebound = v 1 = e ⁡ u ⁡ = e ⁡ 2 gh The height h 1 to which it rises after first rebound h ⁡ 1 = v 1 2 2 g = e ⁡ 2 · 2 gh 2 g = e ⁡ 2 h ⁡ The velocity v 2 after second rebound v 2 = ev 1 = e 2 u The height h 2 it rises after second rebound h ⁡ 2 = v