Chapter 5, Problem 13P

The velocity v of a falling parachutist is given by

$v=\frac{gm}{c}\left(1-e^{-\left(c/m\right)t}\right)$

where $g=9.81{\text{ m/s}}^2$. For a parachutist with a drag coefficient $c=15$ kg/s, compute the mass m so that the velocity is $v=36\text{ m/s at }t=10\text{ s}$. Use the false-position method to determine m to a level of ${\epsilon }_s=0.1\%$.