Question

22 multiple choice 1 point
consider the following physical situation. for each case, determine the angle between the indicated force (in boldface type) and the displacement (\theta\ in the work equation).
the force of air resistance acts upon a vertically - falling skydiver.
0°
90°
30°
180°

Explanation:

When a skydiver is falling vertically, the force of air resistance acts in the opposite direction to the skydiver's motion (displacement). In the work - equation \(W = Fd\cos\theta\), when two vectors (force and displacement vectors in this case) are in opposite directions, the angle \(\theta\) between them is \(180^{\circ}\) because \(\cos\theta=\frac{\vec{F}\cdot\vec{d}}{\vert\vec{F}\vert\vert\vec{d}\vert}\), and for opposite - direction vectors \(\vec{F}\cdot\vec{d}=-\vert\vec{F}\vert\vert\vec{d}\vert\), so \(\cos\theta=- 1\) and \(\theta = 180^{\circ}\).

Answer:

\(180^{\circ}\)