A ball is thrown straight up and rises to a maximum height of 21 m above the ground. At what height is the speed of the ball equal to half of its initial value? Assume that the ball starts at a height of 1.9 m above the ground.
When the speed is half of the initial value, the kinetic energy will be 1/4 of the original value, because K.E. is proportional to V^2.
At 1/4 of the initial K.E., 3/4 of the initial kinetic energy will have been converted to potential energy, and the ball will have risen 3/4 of its maximum amount. Since the maximum rise is 19.1 m, it will have risen 14.44 m above the starting point.
Add that to 1.9 m for the answer, measured from above ground.