Optimization Problem

Question

The range R of a projectile fired with with constant velocity v at an upward launch angle of A is given by:  . In this formula g is the acceleration due to gravity, which is constant near Earth's surface. Find the angle A at which the projectile's range is a maximum.

Answer 1

Simply differentiate R with respect to A and set the derivative equal to 0.

You should find the cos 2A = 0 which makes the angle at which the range is maximum = to pi/4..