Chapter 1, Problem 37P

The velocity v and the falling distance d as a function of time of a skydiver that experience the air resistance can be approximated by:

and $d(t)=\frac{m}{k}\ln \left[cosh\left(\sqrt{\frac{kg}{m}t}\right)\right]$

where k = 0.24 kg/in is a constant, in is the skydiver mass, g = 9.81 m/s² is the acceleration due to gravity, and s is the time in seconds since the skydiver starts falling. Determine the velocity and the falling distance at t=8 s for a 95-kg skydiver

$v(t)=\sqrt{\frac{mg}{k}\tanh }\left(\sqrt{\frac{kg}{m}t}\right)$