A baseball pitcher can throw a ball more easily horizontally than vertically. Assume that...

A baseball pitcher can throw a ball more easily horizontally than vertically. Assume that the pitcher’s throwing speed varies with elevation angle approximately as , where θ0 is the initial elevation angle and v0 is the initial velocity when the ball is thrown horizontally. Find the angle θ0 at which the ball must be thrown to achieve maximum (a) height and (b) range.

Find the values of the maximum (c) height and (d) range. Assume no air resistance and let v0 = 25 m/s.