Question

You go skydiving. Unfortunately, your parachute doesn't open. To try slow yourself down you spread your arms and legs out, so that your effective size becomes like a rectangle of height 1.8 m and width of 0.5 m. What is your terminal velocity if you have a mass of 65 kg? (Hint: set drag coefficient, C=1)

a) 15mph

b) 98 mph

c) 76mph

Answer 1

There are two forces acting: mg is the gravitational force of the Earth and F_drag is the drag force of the air. The free-body diagram is shown below

The drag force is given by

where C is the drag coefficient, A is the effective area, p is the density of air, v is the speed of the person.

There is no change in velocity when the terminal velocity is obtained. The acceleration of the person is zero. By Newton's second law of motion, the net force acting on the person must be zero. In other words, the terminal velocity is obtained when the drag force is equal to the gravitational force.

Substituting we get

We know that and