Air resistance: 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

Terminal speed occurs when the drag force is equal to the weight of the object, thus we can use the equation below to find the constant of proportionality:

mg = kv^2

where m = 20.0 kg is the mass of the object, g = 9.81 m/s^2 is the acceleration due to gravity, and v = 80.0 m/s is the terminal speed. Solving for k:

k = mg/v^2 = (20.0 kg)(9.81 m/s^2)/(80.0 m/s)^2 = 0.3075 N·s^2/m^2

Now, we can use the same equation to find the drag force at a speed of 30.0 m/s:

Fdrag = kv^2 = (0.3075 N·s^2/m^2)(30.0 m/s)^2 = 277.5 N

Therefore, the magnitude of the drag force on the object when it is falling with a speed of 30.0 m/s is 277.5 N, which is closest to choice D, 73.5 N.

Air Resistance: the Magnitude of the Drag Force of Air