Perform a simulation using MATLAB$/$Simulink that captures the dynamic behavior of dropping a

racquetball from the top of a building $($similar to the Empire State Building$),$ as shown below, using the

linear air drag$/$friction model. The goal is to determine: a$)$ the time that it takes the ball to hit the ground,

and b$)$ the velocity at which the ball hits the ground. You will need to perform the followings tasks:

a$.$ Derive a differential equation that describes the dynamic behavior of the ball, in terms of the

variable y$\_1$ and its derivatives. The tell$-$tale for y$\_1$ is located at the top of the building.

b$.$ Implement a solution for the differential equation that you derived using Simulink. Incorporate a

mechanism in the model so that the simulation stops when the ball hits the ground $($I recommend

that you do it without first looking at the Simulink implementation shown in the Reference

Section. And then, once you are finished, you can look at it to confirm$).$ Also use the $$Display$$

icon. It displays the value of the time variable when the simulation stops. Also the clock icon

produces the time variable during the simulation.

c$.$ Simulate the system. Make sure that you get the same results of the simulation shown in the

Reference section. Provide a screen shot of your parameter file $($i$.$e$.$ a script file$),$ and the Simulink

diagram, using the $$Display$$ icons.$\%$ parameter$\_$FSS$.$m

$\%$ this script file contains all the parameter values for the racquetball:

$m=\frac{30}{{454}^{**}32\mathrm{.}2}$;$\%$ mass of racquetball in slugs $($In the CGS system, it is $30g)$

$g=32\mathrm{.}2,$;$\%$ acceleration of gravity in $f\frac{t}{s^{{?}^{{?}^{?}}}}2$

$b=0\mathrm{.}00097**1,$;$\%$ air friction in $lb\frac{f}{f\frac{t}{s}}$

$\%$ STOP SIMULATION

y$\_$stop $=1250$;$\%$ y final value, used to stop simulation, $ft$