Exercise taken from Paul L DeVries $-$ A first course in computational physics $(1984).$ Please create a $.$f$95$ program that solve this problem.

EXERCISE $5\mathrm{.}5$

One of the standard problems of first$-$year physics is one$-$dimensional projectile motion $-$ but contrary to standard practice, let's include air resistance to see how large an effect it is$.$ The time rate of change of the momentum is

$\frac{dp}{dt}=mg-k{v}^2$

where $m$ is the mass of the object, $g=9\mathrm{.}8\frac{m}{s^2}$ is the acceleration due to gravity, and $k$ is a drag coefficient. For a particular sphere of mass ${10}^{-2}kg$ the drag coefficient was determined to be $k={10}^{-4}k\frac{g}{m}.$ Letting $p=mv,$ use the fourth$-$order Runge$-$Kutta method to find the velocity of the sphere released from rest as a function of time for $0$ seconds. Choose a step size $to$ ensure $4-$significant$-$digit accuracy. Compare your calculation $to$ the zero$-th$ order approximation, $e.g.,$ the analytic solution obtained $by$ ignoring air resistance.