Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-A pilot wants to fly on a bearing of $60.9 ^ { \circ }$. By flying due east, he finds that a $57 - \mathrm { mph }$ wind, blowing from the south, puts him on course. Find the ground speed of the plane.
A) $117 \mathrm { mph }$
B) $176 \mathrm { mph }$
C) $65 \mathrm { mph }$
D) $234 \mathrm { mph }$

Question

Quizplus · Accepted Answer

To solve this, we use vector addition. The wind provides a force to the east, and the plane's intended direction is $60.9^\circ$ north of east. We can decompose the plane's velocity into two components: one in the direction of the wind (east) and one perpendicular to it (north). The eastward component must counteract the wind's velocity to maintain the desired bearing, meaning the plane's eastward speed relative to the ground is the sum of its own velocity in that direction and the wind's velocity. Using trigonometry, specifically the sine function for the angle given, we can find the plane's ground speed (the hypotenuse of the triangle formed by the velocity components) is approximately 117 mph, considering the wind's effect and the desired bearing.

Use the Parallelogram Rule to Find the Magnitude of the Resultant