An airplane flies 120 km at a constant altitude in a direction 30.0° north of east.A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west.How much work is done on the plane by the air? A) -2.71 × 10⁸ J B) -0.985 × 10⁸ J C) -221 × 10⁸ J D) 221 × 10⁸ J E) 0.821 × 10⁸ J

Question

Quizplus · Accepted Answer

The work done by a force is given by the formula $W = Fd\cos(\theta)$, where $F$ is the magnitude of the force, $d$ is the distance over which the force acts, and $\theta$ is the angle between the force direction and the direction of motion. Here, the force is 2.40 kN (2400 N) and the distance is 120 km (120,000 m). The angle between the direction of the force (10° south of west) and the direction of the plane's motion (30° north of east) is 180° - (30° + 10°) = 140°. Thus, $W = 2400 \times 120,000 \times \cos(140°)$, which results in a negative value because the force is acting opposite to the direction of motion, indicating that the work done by the air on the plane is negative.

An Airplane Flies 120 Km at a Constant Altitude in a Direction