STATEMENT OF PROBLEM

The table below gives approximate terminal velocities of a sky diver:

Diver's Position terminal velocity

Vertical With Hands at Side
(feet pointing at ground): 278.8 ft/sec

Horizontal (spread eagle --
body parallel to ground): 180.4 ft/sec

With Chute Open (diver
vertical): 21.32 ft/sec

A sky diver weighs 130 pounds and her pack weighs an additional 25 pounds. She falls from a plane flying at 5000 feet.

(1) Assuming that the drag due to wind resistance is proportional to her speed, determine three differential equations which account for her velocity in each phase of flight.

(2) Utilize the equations found in (1) to determine how long it will take for the sky diver to hit the ground if she drops from 5000 feet vertically, at first with her body pointing downward, and then drops with her body parallel in "spread eagle" fashion from 3000 feet down to 500 feet where she opens her chute.

(3) Further modify your model to account for non-instantaneous changes between stages of flight.