Bouncing Balls

Question 1. Figure 1 shows what happens when I drop a ball from 100 metres and it bounces back to 50 metres after the first bounce. How far will the ball travel in total after all subsequent bounces?

Question 2 (Harder). Figure 2 shows what happens if the platform on which I drop the ball starts moving upwards at the moment I drop the ball. If the platform moves at a constant speed of 1 metre per sec, will the total distance the ball travels in all bounces be greater or less than the total distance the ball travels in Question 1? (I consider the ball to stop bouncing at the bounce at which the platform catches up with ball before the ball reaches its highest point.)

Question 3 (Harder). At what speed would the platform need to be moving so that the platform catches up with the ball before the ball reaches its highest point on the first bounce?

Question 4. What are your answers to questions 1, 2 and 3 if I drop the ball from only 2 metres?

Question 5 (New assumptions). What if the platform is a lift already moving upwards at 1 metre/sec when I drop the ball from 2 metres whilst travelling in the lift. How far does the ball travel relative to the lift floor?

Answers to John Rowland