PROBLEM 38E

Skydiving A skydiver weighs 125 pounds, and her parachute and equipment combined weigh another 35 pounds. After exiting from a plane at an altitude of 15,000 feet, she waits 15 seconds and opens her parachute. Assume that the constant of proportionality in the model in Problem 35 has the value k = 0.5 during free fall and k = 10 after the parachute is opened. Assume that her initial velocity on leaving the plane is zero. What is her velocity and how far has she traveled 20 seconds after leaving the plane? See Figure 3.1.11. How does her velocity at 20 seconds compare with her terminal velocity? How long does it take her to reach the ground? [Hint: Think in terms of two distinct IVPs.]

Solution:

Step 1:

The differential condition that portrays a falling items with air resistance corresponding to the quick speed is:

Where m is mass, g is gravity (32 ft/sec2) and k is the proportionality constant of air resistance. In this condition the descending heading is certain.