please show the simulink model and equations used to create the simulation A team of engineering students is planning to sign up at the $$Bungee Adventures$$ to jump off giant $200$ ft

$(60\mathrm{.}9$ m$)$ tall trees in a Redwood Forest this summer. Here is the Bungee Adventures website: Bungee

Adventures $$ On the other side of every fear is a freedom

Three bungee videos: Tree Bungee $$ Bungee Adventures

The students in this group weigh between $50$ kg $(110$ lbs$.)$ and $90$ kg $(200$ lbs$.).$ This is a dangerous adventure.

It is important to analyze the bungee jumping details for a $50-$kg mass and a $90-$kg mass using a $10-$meter

long bungee line prior to jumping off a rope tight between trees in person.

The equation to use for the analysis is Newton$$s Second Law,

F $=$ ma

where F is the sum of the gravitational, aerodynamic drag, and bungee forces acting on the jumper, m is the

mass of the jumper, and a is the acceleration.

Define the distance the jumper falls as the variable x$.$ Distance is a function of time, x$($t$).$ The jumper$$s

velocity and acceleration are then represented as x$$ and x$,$ respectively. The Newton$$s equation to solve for

acceleration is:

x$=$ F $/$ m

Next, determines the forces making up F$.$

The gravitational force will be the jumper$$s weight, which is:

W $=$ m g

g is about $9\mathrm{.}81$ m$/$s$2$ at the surface of the earth.

The aerodynamic drag, D$,$ will be proportional to the square of the jumper$$s velocity,

D $=$ c $($x$)2$

The constant c can be computed from the $55$ m$/$s free$-$fall terminal velocity. At $55$ m$/$s$,$ the aerodynamic drag is

equal to the weight of the jumper, so c can be determined using:

c $=$ D $/($x$)2=$ W $/(55$ m$/$s$)2$

Finally, after the jumper has fallen beyond the bungee cord length, the slack in the bungee will be eliminated,

and it will begin to exert an arresting force, B$,$ of $60$ N for every meter that it is stretched beyond $10$ m$.$

B $=60($x $-10)$

The bungee also has a viscous friction force, R$,$ once it begins to stretch, which is given by:

R $=3$ x$$

Thus, there will be two equations for computing the acceleration. The first equation will be used when the

distance x is less than or equal to $10$ m:

x$=$ F $/$ m $=($W $$ D$)/$ m

A second equation will be used when x is greater than $10$ m:

x$=$ F $/$ m $=($W $$ D $$ B $$ R$)/$ m

Simulation:

$$ Create one Simulink MATLAB Function model $($using the MATLAB Function block$)$ to simulate a $50$

kg person bungee jumping $[4$ pt$]$ off the tree for the first $300$ seconds $[1$ pt$].$

$$ Add mux $[1$ pt$],$ display $[1$ pt$],$ scope $[1$ pt$],$ and $$To File$[2$ pt$]$ blocks in the Simulink model to save the

simulation result, the simulation time $($t$),$ distance $($x$)[1$ pt$],$ velocity $($x$)[1$ pt$]$ and acceleration $($x$)[1$ pt$]$

to a $.$mat file.

$$ Adjust the Simulink model$$s maximum step size to $0\mathrm{.}1$ or smaller $[1$ pt$]$ to ensure the simulation will

compute enough points for obtaining accurate maximum and minimum values of the simulation.

$$ Create another Simulink model to simulate a $90$ kg person bungee jumping $[4$ pt$]$ off the tree for the

first $300$ seconds $[1$ pt$].$

$$ Add mux $[1$ pt$],$ display $[1$ pt$],$ scope $[1$ pt$],$ and $$To File$[2$ pt$]$ blocks collect the Simulink simulation data,

the simulation time $($t$),$ distance $($x$)[1$ pt$],$ velocity $($x$)[1$ pt$]$ and acceleration $($x$)[1$ pt$]$ to a $.$mat file.

$$ Adjust the Simulink model$$s maximum step size to $0\mathrm{.}1$ or smaller $[1$ pt$]$ to ensure the simulation will

compute enough points for obtaining accurate maximum and minimum values of the simulation.

$$ Create a MATLAB program that will automatically open both Simulink models $[2$ pt$]$ and run both

Simulink models $[2$ pt$].$ Load both $.$mat files generated by the Simulink models to the MATLAB

program. Extract t $[2$ pt$],$ x $[2$ pt$],$ x$[2$ pt$],$ and x$[2$ pt$]$ from the Simulink results.

$$ Add a MATLAB built$-$in ode$45$ function $[2$ pt$]$ in the MATLAB program to integrate the $50$ kg person

bungee jumping equations $[4$ pt$].$ Obtain distance $($x$)[1$ pt$],$ velocity $($x$)[1$ pt$],$ and compute acceleration

$($x$)[4$ pt$]$ for the first $300$ seconds $[1$ pt$].$

$$ Add another MATLAB built$-$in ode$45$ function $[2$ pt$]$ in the MATLAB program to integrate the $90$ kg

person bungee jumping equations $[4$ pt$].$ Obtain distance $($x$)[1$ pt$],$ velocity $($x$)[1$ pt$],$ and compute

acceleration $($x$)[4$ pt$]$ for the first $300$ seconds $[1$ pt$].$

$$ Generate one figure $[2$ pt$]$ that contains $3$x$2$ subplots $[2$ pt$]$ to plot and compare the $50$ kg person

bungee jumping Simulink solution and the $50$ kg person bungee jumping ode$45$ solution side$-$by

side.

The figure should include the following:

o Plot the bungee jumper$$s distance $($x$)$ vs$.$ t chart with the Simulink Solution on the left $[1$ pt$]$ and

plot the x vs$.$ t chart using the ode$45$ solution on the right $[1$ pt$].$

o Plot the bungee jumper$$s velocity $($x$)$ vs$.$ t chart with the Simulink Solution on the left $[1$ pt$]$

and plot the x$$ vs$.$ t chart using the ode$45$ solution on the right $[1$ pt$].$

o Plot the bungee jumper$$s acceleration $($x$)$ vs$.$ t chart with the Simulink Solution on the left $[1$

pt$]$ and plot the x$$ vs$.$ t chart using the ode$45$