At a given instant t$0,$ a $1000-$kg earth$-$orbiting satellite has the inertial position and velocity vectors

r$0=3207$i $+5459$j $+2714$k $($km$)$

v$0=6\mathrm{.}532$i $+0\mathrm{.}7835$j $+6\mathrm{.}142$k $($km$/$s$).$

Solve

$$r $=\backslash$mu

r$3$ r

$1$

numerically to find the maximum altitude reached by the satellite and the time at which it occurs.

You may start with the orbit.m MATLAB program $($provided on Canvas$)$ and modify it to get the

answers, or write your own program.

$($For MEEM$5720$ students, I encourage you $($but not required$)$ to write your own program to

solve this problem. If you use MATLAB, ode$45$ may be a good option to use.