Solve the Problem $\theta$ That a Shot-Putter Should Aim for in Order to Throw

Solve the problem.
-The optimal angle of elevation $\theta$ that a shot-putter should aim for in order to throw the greatest distance depends on the velocity $\mathrm { v }$ of the throw and the initial height $h$ of the shot. One model for $\theta$ that achieves this maximum distance is $\theta = \sin ^ { - 1 } \left( \sqrt { \frac { \mathrm { v } ^ { 2 } } { 2 \mathrm { v } ^ { 2 } + 64 \mathrm {~h} } } \right)$ . Suppose a shot-putter can consistently release the steel ball with velocity of 40 feet per second from an initial height $h$ of $5.7$ feet. What angle, to the nearest degree, will maximize the distance?

A) $46 ^ { \circ }$
B) $42 ^ { \circ }$
C) $68 ^ { \circ }$
D) $64 ^ { \circ }$

Correct Answer:

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