A Woman at a Point $A$ On the Shore of a Circular Lake with Radius

question 76

Multiple Choice

A woman at a point $A$ on the shore of a circular lake with radius $4 \mathrm { mi }$ wants to arrive at the point $C$ diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of $6 \mathrm { mi } / \mathrm { h }$ and row a boat at $2 \mathrm { mi } / \mathrm { h }$ . How should she proceed? (Find $\theta$ ) . Round the result, if necessary, to the nearest hundredth.

• A) \(\quad 0.62\) radians
• B) \(0.44\) radians
• C) \(0.46\) radians
• D) She should walk around the lake from point A to point C.
• E) She should row from point A to point \(C\) radians

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Definitions:

Palatoglossus

A muscle that elevates the back of the tongue and narrows the oropharyngeal isthmus, playing a role in swallowing and speech.

Soft Palate

The fleshy, flexible part toward the back of the roof of the mouth, separating the mouth from the pharynx.

Sternocleidomastoid

A muscle in the neck that runs from the sternum and clavicle to the mastoid process of the temporal bone, involved in rotating and flexing the head.

Sternal End

The part of a bone that is located nearest to the sternum, often referring to the end of the clavicle that articulates with the sternum.