A satellite of mass M is launched vertically upwards with an initial speed u from the surface of the earth.…

$\frac{-{\mathrm{GM}}_{\mathrm{e}}\mathrm{M}}{\mathrm{R}}+\frac{1}{2}{\mathrm{Mu}}^2=\frac{-{\mathrm{GM}}_{\mathrm{e}}\mathrm{M}}{2\mathrm{R}}+\frac{1}{2}{\mathrm{Mv}}^2$

${\mathrm{V}}_{\tau }\to$ Transverse velocity of rocket 
${\mathrm{V}}_{\mathrm{R}}\to$ Radial velocity of rocket

$V=\sqrt{\frac{G{M}_e}{2R}}$

$\frac{M}{10}{V}_T=\frac{9M}{10}\sqrt{\frac{G{M}_e}{2R}}$
$\frac{\mathrm{M}}{10}{\mathrm{V}}_{\mathrm{r}}=\mathrm{M}\sqrt{{\mathrm{u}}^2-\frac{{\mathrm{GM}}_{\mathrm{e}}}{\mathrm{R}}}$

Kinetic energy $=\frac{1}{2}\frac{\mathrm{M}}{10}\left({\mathrm{V}}_{\mathrm{T}}^2+{\mathrm{V}}_{\mathrm{r}}^2\right)=\frac{\mathrm{M}}{20}\left(81\frac{{\mathrm{GM}}_{\mathrm{e}}}{2\mathrm{R}}+100{\mathrm{u}}^2-100\frac{{\mathrm{GM}}_{\mathrm{e}}}{\mathrm{R}}\right)$

$=\frac{M}{20}\left(100u^2-\frac{119G{M}_e}{2R}\right)$
$=5\mathrm{M}\left({\mathrm{u}}^2-\frac{119{\mathrm{GM}}_{\mathrm{e}}}{200\mathrm{R}}\right)$