A ball is allowed to fall a height of 15 m. Calculate the velocity with which it strikes the ground. To what height will the ball re-bounced if it...

Hello!

The speed of a falling ball is  downwards, where g is the gravity acceleration. The height of a falling ball is

where is the initial height.

A ball strikes the ground when H(t)=0, so

and the speed will be This is the answer to the first part.

The kinetic energy before the strike is at the end of the re-bouncing it will be zero. The change of the potential energy will be , where is the maximum height after the re-bouncing. So

or

This is the answer for the second part.

That said, the first part could be solved quickier using energy considerations (potential energy becomes kinetic), and the second - considering the potential energy before the fall :)