I want you to solve this problem with runge$-$ kutta method. I want du have every detail and to solve the problem in matlab. I also want you to give me the code for solving the problem.

A small rocket stands on a table and is about to take off for a flight. The flight is described by the following system of differential equations:

m $$x $=$ F cos$(\backslash$phi $)$ kx $$xV

m $$y $=$ F sin$(\backslash$phi $)$ ky $$yV $$ mg

V $=$x$2+$y$2$

mx$=$Fcos$(\backslash$phi $)-$kxx$$V

my$=$Fsin$(\backslash$phi $)-$kyy$$V$-$mg

V$=$x$2+$y$2$

where y represents the height and x represents sideways displacement. The dots denote time derivatives, the gravitational constant is g$=9\mathrm{.}82$m$/$s$2,$ and $\backslash$phi is the angle of the rocket with respect to the horizontal plane given by $\backslash$phi $=$arctan$($y$/$x$).$ The constants kx$=$ky$=0\mathrm{.}001.$

The rocket's mass decreases as its fuel burns up according to m$($t$)=$m$0$kt until all the fuel has burned up at t$=0\mathrm{.}08$ seconds, where m$0=0\mathrm{.}050$ and k$=0\mathrm{.}08.$ It starts with an initial velocity of $20$m$/$s from the table $(!)$ at an angle of $80$ degrees with respect to the table surface. As long as the fuel burns, F$=1,$and afterward, F$=0$

a$)$ What is the maximum height the rocket reaches?

b$)$ How far has the rocket traveled sideways when it lands? $($i$.$e$.,$ the x$-$value. Assume the table surface is horizontal$).$

c$)$ To avoid damaging the table, the rocket should land at x$=8\mathrm{.}5$ We want to adjust the value of F to achieve this. What value must F have when the fuel is burning? d$)$ We also want a certain maximum height. Adjust and determine the values of F and the initial angle so that the rocket's highest height becomes $15$ and it lands at $7\mathrm{.}5$ meters. Do not forget matlab.$m{x}^{}=$Fcos$()-k_x{x}^{}V$

$m{y}^{}=$Fsin$()-k_y{y}^{}V-mg$

$V=\sqrt[\phantom{2}]{x^{}{?}^2+y^{}{?}^2}$

Send me the complete code and the answers of a$,$b$,$c$,$d shall be displayed.