The goal of this assignment is to plot the trajectory of a projectile given an initial launch velocity and angle.

It will require user inputs for initial velocity $($m$/$s$)$ and angle $($degrees$),$ time step definition, and plotting of

projectile path $($vertical distance vs horizontal distance$).$ Additionally, identify the maximum altitude and

horizontal distance traveled. You will write code for this assignment in Python and Matlab.

Python Instructions

$1.(10$ points$)$ Create user inputs for initial velocity and launch angle and set equal to variables $$V$$

and $$angle$.$ Define a variable $$g$$ for gravity constant $($g $=9\mathrm{.}8$ m$/$s$2$

$).$

$2.(10$ points$)$ Define time step using numpy.linspace$()($ex: timestep $=$ numpy.linspace$()).$ This will

create a time step array for the present problem definition. I suggest using $0-5$ seconds as a starting

point and adjust as needed. $($You will need to adjust your code to handle large velocities, so a

larger timestep will be needed. Your code should be able to accept and process such extreme

velocity and launch angles, e$.$g$.1000$ m$/$s @ $60$ deg angle, etc$)$

$3.(30$ points$)$ Using kinematic equations, determine the horizontal and vertical positions for the

projectile. $**$Remember to convert from degrees to radians when using math.sin$()$ and math.cos$(),$

etc.

hPos $=$ V$*$cos$($angle$)*$timestep

vPos $=$ V$*$sin$($angle$)*$timestep $(0\mathrm{.}5*$g$*($timestep$**2))$

$4.(10$ points$)$ Determine the maximum altitude achieve using:

vMax $=$ max$($vPos$)$

$5.(10$ points$)$ Determine the maximum horizontal distance traveled before projectile hits ground

level. Use the following equations:

time $=2*$V$*$sin$($angle$)/$g

hMax $=$ V$*$cos$($angle$)*$time

$6.(30$ points$)$ Plot the projectile path, vMax, hMax using plt$.$plot$().$ Use line$/$marker styling as needed.

Add axis labels and title, adjust axis boundaries as needed.

Matlab Instructions

$7.(10$ points$)$ Create user inputs for initial velocity and launch angle and set equal to variables $$V$$

and $$angle$.($ex: V $=$ input$($Enter initial velocity in m$/$s: $))$ Also define gravity by: g $=9\mathrm{.}8$

$8.(10$ points$)$ Define time step $[$start:step:end$],($ex: timestep $=[0$:$0\mathrm{.}5$:$2]$ will create a timestep array

of $[00\mathrm{.}511\mathrm{.}52].$ I suggest using $[0$:$0\mathrm{.}05$:$5]$ as a starting point and adjust as needed.

$9.(30$ points$)$ Using kinematic equations, determine the horizontal and vertical positions for the

projectile.

hPos $=$ V$*$cosd$($angle$)*$timestep

vPos $=$ V$*$sind$($angle$)*$timestep $(0\mathrm{.}5*$g$*($timestep$.^2))$

Note: use $.^$ when squaring individual values from the timestep array.

$10.(10$ points$)$ Determine the maximum altitude achieve using:

vMax $=$ max$($vPos$)$

Note: max$()$ is a function built into Matlab.

$11.(10$ points$)$ Determine the maximum horizontal distance traveled before projectile hits ground

level. Use the following equations:

time $=2*$V$*$sind$($angle$)/$g

hMax $=$ V$*$cosd$($angle$)*$time

$12.(30$ points$)$ Plot the projectile path, vMax, hMax using plot$().$ Use line$/$marker styling as needed.

Add axis labels and title, adjust axis boundaries as needed. Example:

plot$($hPos$,$vPos,$\text{'}.$b$\text{'},$hMax,$0,\text{'}$rX$\text{'},$hMax$/2,$vMax,$\text{'}$rX$\text{'},$'LineWidth', $3,$'MarkerSize',$12)$

xlabel$(\text{'}$Horizontal Distance, meters'$)$ ylabel$(\text{'}$Altitude$,$ meters'$)$

title$(\text{'}$Projectile Trajectory'$)$ axis$([0$ hMax$+50$ vMax$+5])$

$13.$ Save your program files $(.$py and $.$m$)$ and plot images $(.$png$)$ to a single folder, zip and upload to

Blackboard by $11$:$59$p$.$m$.$ on April $28,2024($Follow file naming convention in syllabus$).$