Exercise 1.7: Trajectory of a shot

Modify your code so that the 2d trajectory of an object can be computed, and graphs of $y$ as a function of $x$ can be made.

1. As a check on your program, first neglect the effect of air resistance so that you an compare to known results. Supouse that the object is thrown and $t_0$ with an angle $\theta _0$ with an initial velocity $v_0=15$m/s. Vary $\theta _0$ and show that the maximum range occurs at $\theta_0=45^{\circ}$ Compare your result with the exact value $v_0^2/g$

2. Consider the effects of air resistance. Compute the maximum range, and the corresponding angle using $k/m=0.1$, $v_0=30$m/s.