Answer
$1.6~km/s$
Work Step by Step
We can determine the required minimum increment in speed as follows:
$v_c=\sqrt{\frac{GM_e}{h+r_e}}$
We plug in the known values to obtain:
$v_c=\sqrt{\frac{66.73(10^{-12})\times 5.976(10^{24})}{20(10^6)+6.378\times 10^6}}$
This simplifies to:
$v_c=3888.17m/s$
and $v_e=\sqrt{2\frac{GM_e}{h+r_e}}$
We plug in the known values to obtain:
$v_e=\sqrt{2\frac{66.73(10^{-12})\times 5.97(10^{24})}{20(10^6)+6.378(10^6)}}$
This simplifies to:
$v_e=5498.7m/s$
Now $\Delta v=v_e-v_c$
$\implies \Delta v=5498.7-3888.17=1610.53m/s=1.6~km/s$
