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 hot-air balloon is rising vertically $14 \mathrm { ft } / \mathrm { sec }$ while the wind is blowing horizontally at $2 \mathrm { ft } / \mathrm { sec }$. Find the angle that the balloon makes with the horizontal.
A) $37.6 ^ { \circ }$
B) $8.1 ^ { \circ }$
C) $56.7 ^ { \circ }$
D) $81.9 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude of the resultant force can be found using the Pythagorean theorem, as the vertical and horizontal components are perpendicular. The magnitude is $\sqrt{14^2 + 2^2} = \sqrt{196 + 4} = \sqrt{200} \approx 14.1 \, \text{ft/sec}$ (not directly asked but part of the process). To find the angle $\theta$ with the horizontal, use the tangent function: $\tan(\theta) = \frac{14}{2}$. Solving for $\theta$ gives $\theta \approx 81.9^\circ$.

Use the Parallelogram Rule to Find the Magnitude of the Resultant