How High Will it Bounce?
If I drop a ping pong ball and heavier ball, such as a golf ball from a height of 1m as shown in the diagram, what happens when they hit the ground? How high does the ping pong ball rebound?Hint
Reveal

Hint
Try and break down what happens into a series of steps or ‘events’
What happens when the golf ball hits the gound? And how does this ‘look‘ from the reference frame of the pingpong ball... ) Then transform back into the lab frame.....
Solution
Reveal

Solution
The golf ball and pingpong ball fall together. When the golf ball hits the ground at speed v, it rebounds and moves upwards at the same speed, and collides with the pingpong ball coming down at speed v.
Transform to the reference frame of the golf ball, which sees a pingpong ball approaching at 2v. The golf ball is infinitely massive compared to the pingpong ball, so the pingpong ball bounces off and moves upwards at speed 2v, relative to the golf ball.
Now transform back to the lab frame: The pingpong ball is moving upwards at 3v. Since energy, and therefore height, is proportional to v squared, the pingpong ball reaches 9 times the initial height! (or rather it would if the ceiling were not in the way...)