November 1996  ICTCM IX (Reno)  6

Example: The Parachute Problem

Kostelich and Armbruster (Addison–Wesley, 1996, p. 109)

The objective of this problem is to calculate some of the relevant quantities for the fall of a skydiver out of an airplane. We use the simplest model of air resistance, in which we suppose that the drag force through air is proportional to the velocity. The relevant differential equation is

v′ = −g − \frac{k}{m} v.

We take the ground as x = 0 and let x > 0 correspond to positions above the ground. As v = x′, a falling skydiver has negative velocity in this coordinate system. The gravitational constant is g and the coefficient of air resistance is k.