Answer
$h=300Km$
Work Step by Step
We can find the required altitude as follows:
$\frac{2GM_M}{r_f}=\frac{2GM_M}{R_M}+v_f^2-v_i^2$
This simplifies to:
$\frac{1}{r_f}=\frac{1}{R_M}-\frac{\frac{3}{4}v_i^2}{2GM_M}$
We plug in the known values to obtain:
$\frac{1}{r_f}=\frac{1}{1.74\times 10^6}-\frac{\frac{3}{4}(1050)}{2(6.67\times 10^{-11})(7.35\times 10^{22})}$
$\frac{1}{r_f}=\frac{1}{2.04\times 10^6}$
$r_f=2.04\times 10^6m$
Now $h=r_E-R_M$
We plug in the known values to obtain:
$h=2.04\times 10^6-1.74\times 10^6=3.0\times 10^5m$
$h=300Km$
