Chapter 27, Problem 30P

Suppose that the position of a falling object is governed by the following differential equation,

$\frac{d^{2}x}{d{t}^2}+\frac{c}{m}\frac{dx}{dt}-g=0$

where $c=$ a first-order drag coefficient $=12.5\text{ kg/s,}m=\text{mass}=70\text{ kg, and }g=$ gravitational acceleration $=9.81{\text{ m/s}}^2$. Use the shooting method to solve this equation for position and velocity given the boundary conditions, $x\left(0\right)=0\text{ and }x\left(12\right)=500$.