Problem $2$:

Let's make a plot that shows the vector velocity of a ball undergoing projectile motion $($neglecting air resistance$).$

Recall the kinematic equations used to calculate the trajectory $($or the $x$ and $y-$positions$)$ of a ball undergoing projectile motion are as follows:

$x=x_0+v_{x0}t$

$y=y_0+v_{y0}t-\frac{1}{2}g{t}^2$

where $x_0$ and $y_0$ are the initial positions in the $x$ and $y$ direction, $v_{x0}$ and $v_{y0}$ are the initial velocities in the $x$ and $y$ directions, and $g=9\mathrm{.}8\frac{m}{s^2}$ is the acceleration of gravity.

Write code that uses a for loop to calculate the $x$ and $y-$positions from $0$ to $2s$ with $t=0\mathrm{.}1s$ and store them in arrays. Set $v_{x0}=v_{y0}=10\frac{m}{s}.$ Plot the $x$ and $y$ positions against one another to produce a curve like the one shown at the end of this problem.

$2$

Copy the code from above and paste it in the code cell below. Change your program so that the magnitude of the initial speed and its angle with respect to ground can be input by the user using an input prompt. Use the speed and angle to calculate the $x$ and $y-$components of the initial velocity $($i$.$e$.,$ calculate $v_{x0}$ and $v_{y0}$ rather than specify them$).$ Use a while loop to calculate how the position of the projectile changes $(x$ and $y$ values$)$ until it hits the ground $($or is very close to hitting the ground$).$ Again, plot the $x$ and $y$ positions against one another to produce a curve like the one shown at the end of this problem.

Copy and paste your code from above into the code cell below. Add code inside your while loop that calculates and stores how the velocity in the $x$ and $y$ direction changes with time.

Next, use quiver to add a few velocity vectors to your plot, so it looks similar to the one below. You should read MATLAB's documentation to learn how to use quiver. You will also need to use hold on and hold off. Galleries like this MATLAB plot gallery can also be helpful for figuring out how to make a particular type of plot.

Finally, add labels to the $x$ and $y$ axis and use xlim and$/$or ylim to improve the appearance of your plot.