$(25$ pts$)$ Consider the following MATLAB code that models the motion of an object falling under the influence of gravity and air resistance:

Solution:

$*$Analytical Solution Formula:

clear all; close all; clc;

$v(t)=\sqrt[\phantom{2}]{\frac{mm}{cd}}*tanh(\sqrt[\phantom{2}]{\frac{p*ct}{m}}*t)$

$\%\%$ Analytical Solution

$\sqrt[\phantom{2}]{\frac{3,81*68,1}{0,25}}$

$g=9\mathrm{.}81$;$\%$ gravity

$m=68\mathrm{.}1$;$\%$ mass

$cd=0\mathrm{.}25$;$\%$ drag coefficient

$t=0$:$1$:$12$;$\%$ time with a step size of $1$ seconds

$v=q,$

$\%\%$ Numerical Solution $($Euler Method$)$

$dt=1$;$\%$ time step $(s)$

$n=\frac{12}{d}t$;

v$1=.q,$ ; $\%$ Preallocate memory for v$1$

for $1=1$ :$n$

$q,v1(i+1)=$

end

$q,$

$\%\%$ Results and Plots

plot ; $\%$ Complete this line with the appropriate data for the analytical solution hold on plot ; $\%$ Complete this line with the appropriate data for the numerical solution grid on legend$(\text{'}$Analytical Solution', 'Numerical Solution'$)$ xjabell please fill in the blanks