Chapter 23, Problem 13P

Recall that for the falling parachutist problem, the velocity is given by

$v\left(t\right)=\frac{gm}{c}\left(1-e^{-\left(c/m\right)t}\right)$ (P23.13.1)

and the distance traveled can be obtained by

$d\left(t\right)=\frac{gm}{c}{\displaystyle {\int }_0^t\left(1-e^{-\left(c/m\right)t}\right)}dt$ (P23.13.2)

Given $g=98.1,m=70$, and $c=12$,

(a) Use MATLAB or Mathcad to integrate Eq. (P23.13.1) from $t=0$ to 10.

(b) Analytically integrate Eq. (P23.13.2) with the initial condition that $d=0$ at $t=0$. Evaluate the result at $t=10$ to confirm (a).

(c) Use MATLAB or Mathcad to differentiate Eq. (P23.13.1) at $t=10$.

(d) Analytically differentiate Eq. (P23.13.1) at $t=10$ to confirm (c).