Question

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

Answer 1

The drag force on the object is 73.5 N.

Step-by-step explanation:

Given that,

Mass of the object, m = 20 kg

It is mentioned that the drag force of air resistance on a object is proportional to its speed i.e.

`F_d=kV`.............(1)

k is constant

Terminal speed of the object, V = 80 m/s

We need to find the magnitude of the drag force on the object when it is falling with a speed 30.0 m/s.

In case of terminal velocity, the drag force is balanced by the gravitational force as :

`mg=kV`

`k=(mg)/(V)\\\\k=(20* 9.8)/(80)\\\\k=2.45`

The drag force at a speed of 30 m/s is :

`F_d=2.45* 30\\\\F_d=73.5\ N`

So, the drag force on the object is 73.5 N. Hence, this is the required solution.