A ball is dropped from rest at a height $h$ above the ground. For the purpose of calculating how fast it will be going at ground level, we will make the potential energy zero there. Let $"h"$ be the height above the ground, $m,$ the mass of the falling object, $g$ the local acceleration of gravity, and $v$ the velocity. Which of these equations is the correct use of conservation of energy to find the velocity at the ground?

$E=\frac{1}{2}m{v}^2$

$E=-mgh$

$0=\frac{1}{2}m{v}^2-mgh$

$0=\frac{1}{2}m{v}^2+mgh$