Chapter 3.2, Problem 26E

Skydiving A skydiver is equipped with a stopwatch and an altimeter. As shown in Figure 3.2.7, he opens his parachute 25 seconds after exiting a plane flying at an altitude of 20,000 feet and observes that his altitude is 14,800 feet. Assume that air resistance is proportional to the square of the instantaneous velocity, his initial velocity on leaving the plane is zero, and g = 32 ft/s².

1. (a) Find the distance s(t), measured from the plane, the sky-diver has traveled during freefall in time t. [Hint: The constant of proportionality k in the model given in Problem 15 is not specified. Use the expression for terminal velocity v_t obtained in part (b) of Problem 15 to eliminate k from the IVP. Then eventually solve for v_t.]
2. (b) How far does the skydiver fall and what is his velocity at t = 15 s?

Figure 3.2.7 Skydiver in Problem 26