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

question 1

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 $h$ 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) \(64 ^ { \circ }\)

Comprehend the geological reasons behind the curvature of island arcs and the spherical shape of Earth affecting geological structures.

Recognize the characteristics and formation processes of hot spots and oceanic plateaus.

Identify different types of islands (e.g., volcanic islands, atolls) and understand their formation mechanisms.

Understand the concepts of seafloor spreading and the age of oceanic crust, including the identification of the youngest and oldest seafloor regions.

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