Solve the Problem $45 ^ { \circ }$ To the Horizontal, with a Muzzle Velocity of 120 Feet

Multiple Choice

Solve the problem.
-A projectile is fired from a cliff 600 feet above the water at an inclination of $45 ^ { \circ }$ to the horizontal, with a muzzle velocity of 120 feet per second. The height $h$ of the projectile above the water is given by $h ( x ) = \frac { - 32 x ^ { 2 } } { ( 120 ) ^ { 2 } } + x + 600$ , where $x$ is the horizontal distance of the projectile from the base of the cliff. How far from the base of the cliff is the height of the projectile a maximum?

A) 712.5 ft
B) 225 ft
C) 937.5 ft
D) 112.5 ft