## Dropping a Ball

What is the height of a ball that is released from rest if the speed of the ball is 17.7 m/s (i.e., 39.6 mi/hr) just before it hits the ground? Neglect air resistance.

**16.0 m**## Approach

Since there is no air resistance, all the potential energy of the ball at the height is converted into kinetic energy.

## Solution

Conservation of mechanical energy says that the total PE and KE is constant. At height h, the potential energy of the ball is mgh (no KE since released from rest) and just before ball hits the ground the kinetic energy is (no PE energy since the height is zero.) Equating m*g*h= 0.5mv^2 , gives h=.5(v^2/g). Putting in the numbers, h = 16.0 m.