A ball is thrown straight upward and rises to a maximum height of 16 m above its launch point. At what height above the launch point has the speed of the ball decreased to one-half of its initial value?

1 answer

At the half-velocity point, the kinetic energy is 1/4 of the maximum value (because it is propotional to V^2). The other 3/4 of the initial energy must be potential energy. Therefore it has risen to 3/4 of its maximum height (12 meters). At maximum height, all energy is potential and kinetic energy is zero.

The answer would be different if the ball had not been thrown vertically.