Chapter 6.10, Problem 95E

Falling body When an object falling from rest encounters air resistance proportional to the square of its velocity, the distance it falls (in meters) after t seconds is given by $d(t)=\frac{m}{k}\ln \left(\cos \left(\sqrt{\frac{kg}{m}}t\right)\right)$, where m is the mass of the object in kilograms, g = 9.8 m/s² is the acceleration due to gravity, and k is a physical constant.

1. a. A BASE jumper (m = 75 kg) leaps from a tall cliff and performs a ten-second delay (she free-falls for 10 s and then opens her chute). How far does she fall in 10 s? Assume k = 0.2.
2. b. How long does it take her to fall the first 100 m? The second 100 m? What is her average velocity over each of these intervals?