A skydiver will reach a terminal velocity when the air drag equals their weight. For a skydiver with high speed and a large body, turbulence is a factor. The drag force then is approximately proportional to the square of the velocity. Taking the drag force to be

and setting this equal to the person’s weight, find the terminal speed for a person falling “spread eagle.” Find both a formula and a number for vt , with assumptions as to size.

Solution 40PE

We are required to equate the drag force with the skydiver’ weight to find the person’s terminal speed. We are also required to find the numerical value of the terminal velocity.

Step 1 of 3

Given:

Drag force

The skydiver will attain terminal velocity when the drag force is equal to the weight of the person.

If is the mass of the person, then his weight .

When the given drag force is equal to the weight,

…..(1)

This is the required formula for the person’s terminal speed.