Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

# Calculating terminal velocity

Experiments show that the force of air friction on a falling object such as a skydiver or a feather can be approximated fairly well with the equation |Fair | = cρAv2, where c is a constant, r is the density of the air, A is the cross-sectional area of the object as seen from below, and v is the object's velocity. Predict the object's terminal velocity, i.e., the final velocity it reaches after a long time.

As the object accelerates, its greater v causes the upward force of the air to increase until finally the gravitational force and the force of air friction cancel out, after which the object continues at constant velocity. We choose a coordinate system in which positive is up, so that the gravitational force is negative and the force of air friction is positive. We want to find the velocity at which

Fair + FW = 0 , i.e.,
cρAv2 - mg = 0 .

Solving for v gives

Last Update: 2010-11-11