Chapter 21, Problem 9P

Suppose that the upward force of air resistance on a fallingobject is proportional to the square of the velocity. For this case, thevelocity can be computed as

$v\left(t\right)=\sqrt{\frac{gm}{c_d}}\tanh \left(\sqrt{\frac{g{c}_d}{m}}t\right)$

where $c_d=a$ second-order drag coefficient.

(a) If $g=9.81{\text{m/s}}^2,m=68.1\text{kg},$ and $c_d=0.25\text{kg/m}$, use analytical integration to determine how far the object falls in 10 s.

(b) Make the same evaluation, butevaluate the integral with the multiple-segment trapezoidal rule. Use a sufficiently high n that you get three significant digits of accuracy.