The magnitude of the drag force of air resistance on a certain 20.0-kg object is proportional to its speed. If the object has a terminal speed 80.0 m/s, what is the magnitude of the drag force on the object when it is falling with a speed 30.0 m/s?
A) 196 N
B) 7.50 N
C) 15.0 N
D) 73.5 N
E) 42.7 N

Question

Quizplus · Accepted Answer

Since the magnitude of the drag force is proportional to the speed of the object, we can set up a proportion:
drag force at terminal speed / terminal speed = drag force at 30.0 m/s / 30.0 m/s
Solving for the drag force at 30.0 m/s gives:
drag force at 30.0 m/s = (30.0 m/s / 80.0 m/s) x terminal drag force
drag force at 30.0 m/s = (0.375) x terminal drag force
Substituting the given terminal speed of 80.0 m/s, we get:
drag force at 30.0 m/s = (0.375) x mg
drag force at 30.0 m/s = (0.375) x (20.0 kg x 9.81 m/s^2)
drag force at 30.0 m/s = 73.5 N
Therefore, the answer is D.

The Magnitude of the Drag Force of Air Resistance on a Certain