check the code:

function project$\_5()$

$\%$ PROJECT$\_5$ project$\_5()$ models the path of a projectile launched

$\%$ from a raised platform.

$\%$

$\%$ Name: Adham Elmezayen

$\%$ Date: $3$ October $2024$

$\%$ Class: CMPSC $200$

$\%$ Print the Splash Screen

fprintf$(\text{'}-------------------------------------------------$

$\text{'})$;

fprintf$(\text{'}$Welcome to Projectile Motion Simulation $($Project $5)$

$\text{'})$;

fprintf$(\text{'}-------------------------------------------------$

$\text{'})$;

$\%$ Prompt the user for inputs for velocity, angle, and height above the ground

v$0=$ input$(\text{'}$Enter the initial velocity $($m$/$s$)$: $\text{'})$;

theta $=$ input$(\text{'}$Enter the launch angle $($degrees$)$: $\text{'})$;

h $=$ input$(\text{'}$Enter the height above the ground $($m$)$: $\text{'})$;

$\%$ Convert the launch angle to radians

theta$\_$rad $=$ deg$2$rad$($theta$)$;

$\%$ Decompose the velocity into x and y components

vx$0=$ v$0*$ cos$($theta$\_$rad$)$; $\%$ Horizontal component

vy$0=$ v$0*$ sin$($theta$\_$rad$)$; $\%$ Vertical component

$\%$ Acceleration due to gravity

g $=9\mathrm{.}81$; $\%$ m$/$s$^2$

$\%$ Calculate the time to impact $($t$\_$f$)$ using the quadratic formula

$\%$ The equation is: y$($t$)=$ h $+$ vy$0*$ t $-(1/2)*$ g $*$ t$^2$

$\%$ We set y$($t$)=0$ to solve for t when the projectile hits the ground

$\%$ Coefficients for the quadratic equation: $(1/2)*$ g $*$ t$^2-$ vy$0*$ t $-$ h $=0$

a $=-0\mathrm{.}5*$ g;

b $=$ vy$0$;

c $=$ h;

$\%$ Using the quadratic formula: t $=(-$b $\backslash$pm sqrt$($b$^2-4$ac$))/2$a

discriminant $=$ b$^2-4*$ a $*$ c;

if discriminant $<0$

error$(\text{'}$No real solution for time to impact. Check inputs.$\text{'})$;

end

t$\_$f $=(-$b $+$ sqrt$($discriminant$))/(2*$ a$)$; $\%$ Taking the positive root

$\%$ Create additional time variables for different points

t$\_0=0$; $\%$ Initial time

t$\_1=$ t$\_$f $/4$; $\%1/4$th of the flight time

t$\_2=$ t$\_$f $/2$; $\%$ Half of the flight time

t$\_3=3*$ t$\_$f $/4$; $\%3/4$th of the flight time

t$\_4=$ t$\_$f; $\%$ Final time $($impact$)$

$\%$ Time array

t $=[$t$\_0,$ t$\_1,$ t$\_2,$ t$\_3,$ t$\_4]$;

$\%$ Calculate the five horizontal and vertical positions

x $=$ vx$0*$ t; $\%$ Horizontal position: x $=$ vx$0*$ t

y $=$ h $+$ vy$0*$ t $-0\mathrm{.}5*$ g $*$ t$.^2$; $\%$ Vertical position: y $=$ h $+$ vy$0*$ t $-(1/2)*$ g $*$ t$^2$

$\%$ Calculate the five horizontal and vertical velocities

vx $=$ vx$0*$ ones$($size$($t$))$; $\%$ Horizontal velocity remains constant

vy $=$ vy$0-$ g $*$ t; $\%$ Vertical velocity: vy $=$ vy$0-$ g $*$ t

$\%$ Print the results table

fprintf$(\text{'}$

Projectile Motion Results:

$\text{'})$;

fprintf$(\text{'}$Initial velocity: $\%\mathrm{.}2$f m$/$s

$\text{'},$ v$0)$;

fprintf$(\text{'}$Launch angle: $\%\mathrm{.}2$f degrees

$\text{'},$ theta$)$;

fprintf$(\text{'}$Initial height: $\%\mathrm{.}2$f m

$\text{'},$ h$)$;

fprintf$(\text{'}$

$\%-10$s $\%-10$s $\%-10$s $\%-10$s $\%-10$s

$\text{'},$ 'Time $($s$)\text{'},\text{'}$X $($m$)\text{'},\text{'}$Y $($m$)\text{'},\text{'}$Vx $($m$/$s$)\text{'},\text{'}$Vy $($m$/$s$)\text{'})$;

$\%$ Print the results for each time step

for i $=1$:length$($t$)$

fprintf$(\text{'}\%-10\mathrm{.}2$f $\%-10\mathrm{.}2$f $\%-10\mathrm{.}2$f $\%-10\mathrm{.}2$f $\%-10\mathrm{.}2$f

$\text{'},$ t$($i$),$ x$($i$),$ y$($i$),$ vx$($i$),$ vy$($i$))$;

end