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

question 445

Multiple Choice

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 $\mathrm { h }$ 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 34 feet per second from an initial height $h$ of $6.1$ feet. What angle, to the nearest degree, will maximize the distance?

• A) \(64 ^ { \circ }\)
• B) \(41 ^ { \circ }\)
• C) \(45 ^ { \circ }\)
• D) \(60 ^ { \circ }\)

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