Problem $4$:

The trajectory of an object can be modeled as

$y=(tan{}_0)x-\frac{g}{2v_0^{2}co{s}^2{}_0}{x}^2+y_0$

where $y=$ height $($ m $),{}_0=$ initial angle $($radians$),x=$ horizontal distance $(m),g=$ gravitational acceleration $)=(9\mathrm{.}81\frac{m}{s^2},v_0=$ initial velocity $(\frac{m}{s}),$ and $y_0=$ initial height. Use MATLAB to find the trajectories for $y_0=0$ and $v_0=28\frac{m}{s}$ for initial angles ranging from $15$ to $75$ in increments of $15.$ Employ a range of horizontal distances from $x=0$ to $80$ m in increments of $5$ m $.$ The results should be assembled in an array where the first dimension $($rows$)$ corresponds to the distances, and the second dimension $($columns$)$ corresponds to the different initial angles. Use this matrix to generate a single plot of the heights versus horizontal distances for each of the initial angles. Employ a legend to distinguish among the different cases, and scale the plot so that the minimum height is zero using the axis command.