HW$2-$Q$1)$ MATLAB, PLEASE MAKE CODE COPYABLE

Trajectory of a toy missile

The trajectory of a toy missile in $(x,y)$ coordinates can be modeled as the parabola:

$y(x)=a_2{x}^2+a_{1}x+a_0[1]$

where

$a_2=-\frac{\frac{g}{2}}{v_0^{2}co{s}^2({}_0)}$

$a_1=tan({}_0)$

$a_0=y_0$

and

$y_0=1\mathrm{.}7m$ is the initial elevation,

${}_0$ is the initial angle of the missile in radians,

$v_0=60\frac{m}{s}$ is the initial velocity,

the horizontal distance the missile flies is $310m,$

the missile hits a practice target at $3\mathrm{.}8m$ above the ground.

The missile will be launched on Earth where the acceleration due to gravity is

$9\mathrm{.}81\frac{m}{s^2}.$

a$)$ Since the only unknown in equation $[1]$ is the initial angle, ${}_0,$ rearrange equation $[1]$ to be in

the form of a function of ${}_0$ and plot it for $10{}_{0}75.$ Be sure to label the axes and

turn on the grid $($see help on the grid function$).$ Remember xlabel $(\text{'}\backslash$theta$\text{'})$ will

produce a $$ on the $x$ axis. Even though ${}_0$ is in radians, the $x$ axis should be in degrees.

b$)$ In text write the answer to the question: "How many solutions exist?"

c$)$ Compute an approximation for the appropriate initial angle$($s$){}_0$ at which the missile can

is more than one solution, be sure to find them all. Use the fprintf function to print out

a table like the one shown below. Add a row for each zero of the function. The values in

the columns will be the result of the root using each method.

d$)$ Plot the solutions on the plot of the function of ${}_0$ in the figure from part a$.$ Use an asterisk

for the bisect solution and a circle for the fzero solution. If there is more than one

solution, use a different color for each solution. Be sure to include a legend in the lower

left corner.

e$)$ Plot the trajectory of the toy missile in $(x,y)$ coordinates for all of the solutions obtained

using the fzero function. Put both plots in a single new figure $($not subplot$).$ Be sure to

include a legend with entries for each solution that look like this:

Trajectory for ${}_0=.x^2$