EGR$150$ Computer Methods in Engineering

Fall $2024$

Homework $1$: Projectile Motion

Projectile motion is a classic problem in physics, and it is also a good example of breaking

a seemingly complicated problem down into easy$-$to$-$manage parts. The key is that if air

resistance can be neglected, then vertical and horizontal motion are independent of one

another, and we can work on one at a time.

Components of initial velocity: for a given initial velocity $v_0$ and a firing angle $,$ we can

calculate the initial velocity in the $x$ and $y$ directions using cosine and sine:

$v_{0x}=v_0^{**}cos()$;$,v_{0y}=v_0^{**}sin()$

Flight time: if the projectile follows a parabolic path and lands at the same elevation

$($height$)$ as it was launched, then the governing equation can be simplified as follows

$(g$ is the acceleration of gravity, $y_f$ is final height, $y_0$ is initial height, $t$ is flight time$)$:

$y_f=y_0+v_{0y}^{**}t-{0\mathrm{.}5}^{**}{g}^{**}{t}^2$ simplifies $to{v}_{0y}={0\mathrm{.}5}^{**}g**t,ort=(2^{**}\frac{v_{0y}}{g})$

Distance traveled: the projectile travels at a constant horizontal speed the entire time

it is in the air, so the distance traveled is just: $d=v_{0x}^{**}t$

Assignment

Type "diary YourBlazerID$\_$HW$1\_$diary" in the command window before you begin

working, and "diary off" when you finish. Whenever you start and stop work on the

assignment, do the same thing each time.

Write a script named "YourBlazerID$\_$HW$1.$m$"$ that computes projectile motion using

the following steps and features:

choose camelCase names for all of your variables

include comments for the overall script and for each section

specify initial values of $50\frac{m}{s}$ for initial velocity, $30$ degrees for the firing angle,

and $9\mathrm{.}8\frac{m}{s^2}$ for the acceleration of gravity

$$ calculate the $x$ and $y$ components of the initial velocity

calculate the flight time

calculate the total distance traveled

display the flight time and distance traveled to the command window, and suppress

all other output

Submit files "YourBlazerID$\_$HW$1.$m$"$ and "YourBlazerID$\_$HW$1\_$diary" on Canvas