HW$2-$Q$4)$ MATLAB, PLEASE MAKE CODE COPYABLE

The trajectory of a ball thrown by a right fielder as defined in the $($x$,$y$)$ coordinates can be modeled as:

$y=x(tan(\frac{}{180}{}_0))-\frac{g}{2v_0^{2}co{s}^2(\frac{}{180}{}_0)}{x}^2+y_0$

where the angle at which the ball leaves the right fielder's hand is ${}_0=6,$ the initial velocity is

$v_0=92mph,$ the distance between the right fielder and the catcher is $50m,$ and the throw leaves

the right fielder's hand at an elevation of $2\mathrm{.}1m.$ You must use $g=9\mathrm{.}81\frac{m}{s^2}$ and the following

conversion factors: $1$ mile $=5280$ feet and $1$ meter $=3\mathrm{.}28$ feet.

a$)$ Plot the function using the plot command in figure $1.$ Title the plot "MAE $284,$ Homework $2,$

Problem $4,$ Part a$".$ Use the axis command to change the axis so that the $x$ axis starts at $0$

and goes to $50$ meters and the y axis goes from $0$ to $5m.$

b$)$ If the catcher cannot reach above an elevation of $2\mathrm{.}6m,$ will she catch the ball? Use

conditional statements and an fprintf to display the result $($e$.$g$.$ "The elevation at

$x=xxm$ is $x.xxxxm.$ The catcher CAN$/$CANNOT catch the ball"

where either can or cannot is displayed.$)$

c$)$ Compute the maximum height reached by the ball using each of the following methods. Use

the fprintf function to print the result. For example, "The maximum height

using goldmin is X$.$XXXXXXXX m$".$ Display $8$ digits to the right of the decimal

point. You may create functions for golden$-$section and parabolic interpolation.

i$.$ Golden$-$section search $(\{$:$x_l=9,x_u=49,{}_s=0\mathrm{.}2\%)$

ii$.$ Parabolic interpolation $(x_1=0x_2=21,x_3=49,$ maxiterations $=2)$

iii. MATLAB's fminbond with iterations displayed. Use a range of $0$ to the distance of the

catcher.