save a skydiver

Reducing terminal velocity using a parachute

As mentioned in A Common Sky-dive, it is dangerous for a skydiver to hit the ground faster than about 10 mph. So if the skydiver hits the ground at 140 miles per hour (see Terminal velocity, Question 1), he or she will probably not try another dive. If you are not the kind of person who succeeds at first, don't try skydiving.

We will now add a parachute to slow the fall of the diver to earth. Adding a parachute will effectively reduce the terminal velocity of the skydiver by increasing the drag force acting on the skydiver-parachute combination. The parachute will not significantly change or alter the gravitational force which acts on the skydiver since the weight of the parachute is small relative to that of the skydiver. Only the forces acting on the surface of the skydiver and the deployed parachute will be altered. It is the drag of the parachute that dominates the fall of the skydiver, producing a terminal velocity for the skydiver-parachute combination much smaller than that of the skydiver alone.

The parachute has a drag force Fp equal to

where the drag coefficient kp is
for a parachute 24 ft in diameter.

The terminal velocity of the skydiver with a parachute is therefore

The skydiver with a parachute survives to dive again. Note that
where = the drag force on the deployed parachute (N),
= the drag force on the skydiver without a parachute (N),

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