Question

A ball is raised above the floor such that it has 5.0 J of gravitational potential energy and then allowed to fall. How much kinetic energy will it have just before striking the floors?

Answer 1

According to the law conservation of energy, the total energy of an isolated system remains constant.

The total energy consists of the sum of potential energy $U$ and kinetic energy $K$:

$$E = U+K = mgh + \dfrac{mv^2}{2} = const$$

where $h$ is the height of the ball, $v$ is its speed and $m$ is its mass. Since initially the ball didn't have any speed $v = 0$, the total energy is equal to the potential one.

$$E = U_0 = 5J$$

On the opposite just before striking the floors the ball didn't have any potential energy ($h = 0$ ), thus, its kinetic energy at that moment was equal to the total energy $E$ (that is constant at any time):

$$K = E=5J$$

Answer. 5J.