Computer Problem: Using $((((($MATLAB$))))),$ in this problem you will simulate a firework

starting at the moment of the mid$-$air explosion! You will track the motion of eight firework

sparks that are all initially propelled outward with a speed of $10\frac{m}{s}$ moving in eight

different directions within a single vertical plane. Assume the sparks begin at the same

point in the sky$.$ Suppose each spark has a mass of $10$ grams, feels $9\mathrm{.}81\frac{m}{s^2}$ of gravity, and

experiences a linear air drag of the form $F_{\text{D}\text{r}\text{a}\text{g}}=-c_{s}v.$ In a single plot, show the

trajectories of your eight sparks from the initial explosion to $1\mathrm{.}5$ sec later for two values of

drag; $c_s=0\mathrm{.}001N\frac{s}{m}$ and $0\mathrm{.}01N\frac{s}{m}.$ Explain in words how the visuals of your fireworks

display change as the drag coefficient goes up$.$ Please include your code along with your

plots.

$($a$)$ Sample particle trajectories at $t=1\mathrm{.}5s$

$($b$)$ Particle $(m=10g)$ initial conditions