Solve the problem.
-A pilot wants to fly on a bearing of $60.5 ^ { \circ }$. By flying due east, he finds that a 57 -mph wind, blowing from the south, puts him on course. Find the airspeed of the plane.
A) $50 \mathrm { mph }$
B) $101 \mathrm { mph }$
C) $116 \mathrm { mph }$
D) $151 \mathrm { mph }$

Question

Quizplus · Accepted Answer

The airspeed of the plane can be found using vector addition, where the eastward component of the plane's velocity and the wind's velocity vector combine to give the resultant velocity vector on a bearing of $60.5^\circ$. Since the wind is blowing from the south (directly towards the north) and affects the plane's eastward course, we can form a right-angled triangle with the wind speed as one leg (57 mph), the plane's airspeed as the hypotenuse, and the eastward component of the plane's velocity as the other leg. The angle between the plane's desired course (bearing of $60.5^\circ$) and the east direction is $60.5^\circ$. Using trigonometry, specifically the sine function, $\sin(60.5^\circ) = \frac{57}{\text{airspeed}}$. Solving for the airspeed gives approximately $101 \mathrm { mph }$, making option B correct.

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