Terminal Velocity The autonomous differential equation Where k is a positive...

Terminal Velocity The autonomous differential equation

Where k is a positive constant of proportionality called the drag coefficient and g is the acceleration due to gravity, is a model for the velocity v of a body of mass m that is falling under the influence of gravity. Because the term −kv represents air resistance or drag, the velocity of a body falling from a great height does not increase without bound as time t increases.

(a) Use a phase portrait of the differential equation to find the limiting, or terminal, velocity of the body. Explain your reasoning.

(b) Find the terminal velocity of the body if air resistance is proportional to v ². See pages 22 and 26.