If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body’s velocity t seconds into the fall satisfies the equation

where k is a constant that depends on the body’s aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air’s density.)

a. Draw a phase line for the equation.

b. Sketch a typical velocity curve.

c. For a 110-lb skydiver (mg = 110) and with time in seconds and distance in feet, a typical value of k is 0.005. What is the diver’s terminal velocity? Repeat for a 200-lb skydiver.

Transcribed Image Text:

m ap dt mg - kv², k > 0