(Solved): If air resistance is proportional to the square of the instantaneous velocity, then the velocity \ ...

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 \[ m \frac{d v}{d t}=m g-k v^{2}, \quad k>0 . \] Let \( v(0)=0, k=0.125, m=5 \) slugs, and \( g=32 \mathrm{ft} / \mathrm{s}^{2} \). (a) Use the RK4 method with \( h=1 \) to approximate the velocity \( v(5) \) (b) Use a numerical solver to graph the solution of the IVP on the interval \( [0,6] \). (c) Use separation of variables to solve the IVP and then find the actual value \( v(5) \).