Chapter 6.1, Problem 5QC

  Suppose (unrealistically) in Example 3 that the velocity of the skydiver is 80 m/s. for , and then it changes instantaneously to 6 m/s. for . Sketch the velocity function and, without integrating, find the distance the skydiver falls in 40 s.

Example 3 Skydiving

Suppose a skydiver leaps from a hovering helicopter and falls in a straight line. Assume he reaches a terminal velocity of 80 m/s immediately at t = 0 and falls for 19 seconds, at which time he opens his parachute. The velocity decreases linearly to 6 m/s over a two-second period and then remains constant until he reaches the ground at t = 40 s. The motion is described by the velocity function

     $v\left(t\right)=\{\begin{array}{ll}80\hfill & \text{if}0\le t<19\hfill \\ 783-37t\hfill & \text{if}19\le t<21\hfill \\ 6\hfill & \text{if}21\le t\le 40\hfill \end{array}$

Determine the height above the ground from which the skydiver jumped