Answer
$v_0 = 7.68\times 10^3~m/s$
Work Step by Step
We can find the speed:
$K = \frac{1}{2}mv_0^2 = \frac{GMm}{2r}$
$v_0^2 = \frac{GM}{r}$
$v_0 = \sqrt{\frac{GM}{r}}$
$v_0 = \sqrt{\frac{(6.67\times 10^{-11}~N~m^2/kg^2)(5.98\times 10^{24}~kg)}{6.37\times 10^6~m+4.0\times 10^5~m}}$
$v_0 = 7.68\times 10^3~m/s$
