Aim

Given the initial speed $($m$/$sec$)$ and the launch angle $($in degrees$)$ of a point particle projectile calculate the trajectory $($x and z values, in meters$)$ as a function of time in the presence of air friction.

Background

This question is a generalization of project S$-$Friction$1$D$.$ Almost all instructions are valid here as well.

The equation in this case involves vectors:

ma$($t$)=$mgz$^12\backslash$rho ACdv$2$v$^$

where $\backslash$rho is air density, A is the cross section area of the object, Cd is a geometric constant.

The drag force $($the second term$)$ is always in opposite direction to the velocity.

List of Tasks

Your code should follow the same guidelines as S$-$Friction$1$D but the angle $($in degrees$)$ and the initial velocity $($in m$/$s$)$ have to be inputted.

Your code should produce S$-$fric$2$D$.$dat file with two columns, x and z values in meters.

Hints

Remember that the math.sin$()$ and math.cos$()$ functions work only with angles in radians.

Check the example below and note the asymmetric trajectory due to the air drag.

Allowed Libraries

math

random

mathplotlib.pyplot or any other equivalent plotting library