Chapter 25, Problem 19P

Assuming that drag is proportional to the square of velocity, we can model the velocity of a falling object like a parachutist with the following differential equation:

$\frac{dv}{dt}=g-\frac{c_d}{m}{v}^2$ $t=$

where v is velocity (m/s), $t=$ time (s), g is the acceleration due to gravity (9.81 m/s²), $c_d=$ a second-order drag coefficient (kg/m), and $m=$mass (kg). Solve for the velocity and distance fallen by a 90-kg object with a drag coefficient of 0.225 kg/m. If the initial height is 1 km, determine when it hits the ground. Obtain your solution with (a) Euler's method and (b) the fourth-order RK method.