Suppose the model in Problem 40 is modified so that air resistance is proportional to v2...

Suppose the model in Problem 40 is modified so that air resistance is proportional to v², that is, See Problem 17 in Exercises 1.3. Use a phase portrait to find the terminal velocity of the body. Explain your reasoning.

(reference problem 17 in exercise 1.3)

For high-speed motion through the air—such as the skydiver shown in Figure 1.3.16, falling before the parachute is opened —air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.