Write a MATLAB script that uses a first order explicit discretisation scheme:

$\frac{dV}{dt}$~~$\frac{V(t)-V(t-dt)}{dt}$

to calculate the solution of the following equations for the speed and height of a ball:

$m\frac{dV}{dt}=-mg-\frac{S{C}_D{V}^3}{2|V|},\frac{dh}{dt}=V$

$|V|$ indicates the magnitude of $V.$ The abs$()$ function in MATLAB can be used to calculate this

value. The parameters in the equation are $m=0\mathrm{.}16kg,g=9\mathrm{.}81m{s}^{-2},=1\mathrm{.}225kg{m}^{-3},$

$C_D=1$ and $S=0\mathrm{.}0177m^2.$ The initial speed, speed at time $=0$ seconds, is $10\frac{m}{s}$ and the initial

height of the ball is $1$ m $.$ Calculate the solution until the ball returns to earth, when the height

will be less than or equal to $0$ m $.$

Note that for this problem it is likely your solution will involve growing arrays. For this question

there will be no penalty for this.

a$.$ The script should create plots of your results as a function of time. You do not have to

submit this plot.

b$.$ Explain, using comments within the script, what is a suitable choice for the time step

size and why.