Chapter 9, Problem 42P

The velocity, v, of an object that falls freely due to the Earth gravity can be modeled with the equation:

$m\frac{dv}{dt}=-mg+k{v}^2$

where m is the mass of the object, g = 9.81 m/s², and k is a constant. Solve the equation for v for the case that m = 5kg, k = 0.05kg/m, $0\le t\le 15$ s, and v(0) = 0 m/s. Make a plot of r as a function of time.