Solve the Problem $45 ^ { \circ }$ To the Horizontal, with a Muzzle Velocity of 270 Feet

Multiple Choice

Solve the problem.
-A projectile is fired from a cliff 300 feet above the water at an inclination of $45 ^ { \circ }$ to the horizontal, with a muzzle velocity of 270 feet per second. The height $h$ of the projectile above the water is given by $h ( x ) = \frac { - 32 x ^ { 2 } } { ( 270 ) ^ { 2 } } + x + 300$ , where $\mathrm { x }$ is the horizontal distance of the projectile from the base of the cliff. Find the maximum height of the projectile.

A) $869.53 \mathrm { ft }$
B) $569.53 \mathrm { ft }$
C) $2,008.59 \mathrm { ft }$
D) $1,139.06 \mathrm { ft }$