Question

A boy can throw a ball a maximum horizontal distance of R on a level field. How far can he throw the same ball vertically upward? Assume that his muscles give the ball the same speed in each case. (Use R and g as appropriate in your equation.)

Answer 1

At the optimimum angle (for distance) of 45 degrees, the distance (range) that the ball travels is
R = (V^2)/g

At the optimum angle (for height) of 90 degrees, the maximum vertical height of the ball is
Y = V^2/(2g) = R/2