Write a program motion.py that computes an approximate solution of the Newton equations for

the motion of a projectile of mass $1$ kg$,$ launched at an angle of $45$ degrees with respect to the

ground and initial velocity of $100$ m$/$s$,$ under the action of the Earth$$s gravity, described by a

uniform downward acceleration of $9\mathrm{.}81$ m s

$-2$

$,$ and of a drag force, opposite and proportional to

the velocity with proportionality constant $0\mathrm{.}1$ N s m$-1$

$.$

Derive an approximate solution of the equation of motion by the Euler finite difference method;

thet is$,$ approximating differentials by finite differences. Choose a reasonably small time step.

Compute the trajectory of the projectile from the point of launch $($at ground level$)$ until it hits the

ground, assuming a flat ground surface. Have the program generate two line plots:

$1.$ the trajectory, as y $($vertical coordinate$)$ vs$.$ x $($horizontal$)$

$2.$ the speed $($length of the velocity vector$)$ as a function of time.