Chapter 9.2, Problem 13E

If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from

$m\frac{dv}{dt}=mg-k{v}^2,k>0.$

Let v(0) = 0, k = 0.125, m = 5 slugs, and g = 32 ft/s².

1. (a) Use the RK4 method with h = 1 to approximate the velocity v(5).
2. (b) Use a numerical solver to graph the solution of the IVP on the interval [0, 6].
3. (c) Use separation of variables to solve the IVP and then find the actual value v(5).