Question

john throws two identical balls up into the air. For the balls to have the same amount of gravitational potential energy at a certain point on time, what must be true?

Answer 1

They must be at the same height above the ground.

Answer 2

Since the balls are identical we assume the balls have the same mass
`m`. The gravitational potential energy at any time is given by
`P=mgh`. Where
`g` is acceleration due to gravity and
`h` the height of the ball above the surface of the earth.

For both the balls to have the same potential energy, the height of both the balls above the earth should be the same.