Question

A sky diver whose mass is 90 kg, is falling at a terminal speed of 60 m/s. What is the magnitude of the force of the air on the sky diver?

Short answer

The magnitude of the force of the air on the sky diver is obtained as 882 N .

Step-by-step solution

Define the terminal speed

The outmost velocity (speed) that an item may achieve as it descends through a fluid is called terminal velocity (air is the most common example). It happens when the total of the drag force (Fd) and the buoyancy force (FG) exerted on the item equals the downward force of gravity (FG). The item has no acceleration since the net force on it is zero.

Calculation of magnitude of force

Mass of the sky driver is 90 kg, speed is 60 m/s and gravitational force has a value of 9.8 N/kg .

During the terminal speed, due to the air resistance the gravitational force is balanced making the magnitude of the force of the air on the skydiver equal to the weight of the sky driver.

Equate force of air to the weight of the skydiver and substitute the values.

$$\begin{gathered} F_{air}=W \\ =mg \\ =\left(90\mathrm{kg}\right)\left(9.8\mathrm{N}/\mathrm{kg}\right) \\ =882\mathrm{N} \end{gathered}$$

Therefore, the magnitude of the force is 882 N .