Let U be the projection velocity at bottom of tower. Time taken by the ball and projection velocity U are related by the following equation
Let V be the velocity when it reaches top of tower and h is tower height. we can write the following equation for V
if V is the initial speed for the observer at the top of the tower, the time taken by the ball to reach maximum height from top of the tower can be obtained from the following equation.
By using the equations (2) and (4), one can get