Work: 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?

Question

Quizplus · Accepted Answer

Work done by a force is given by the dot product of the force vector and the displacement vector. The angle between the direction of the force (10° south of west) and the displacement (30° north of east) is 180° - (30° + 10°) = 140°. The work done is W = Fd cos(θ) = 2400 N * 120 km * cos(140°), which results in a negative value because the angle is greater than 90°, indicating that the force is doing negative work on the airplane. The correct calculation leads to the answer in option A.

Work: an Airplane Flies 120 Km at a Constant Altitude