Problem $4\mathrm{.}4($Textbook p$113-)$ For a SpaceX rocket leaving Earth's surface, straight$-$up$,$ at

velocity $v_0,$ derivate the formula of its $($later$)$ velocity as a function of the distance $r$ from

the rocket to the earth's center and the other given parameters: the Earth's radius $R,$ mass

$M,$ and gravitational constant $G.$ Find the minimum $v_0$ at which the rocket can escape the

earth. Of course, this problem is hypothetical as we assumed the "rocket" has no engine

$($and the only push is the initial kinetic energy.$)$