A space ship of mass 2 × 10 ^ 4 kg is launched into a circular...

The orbital velocity of satellite is

${v}_{orb} = \sqrt{\dfrac{GM}{R}}$

The escape velocity is

${v}_{esc} = \sqrt{\dfrac{2GM}{R}}$

Hence, the additional velocity required is

$\Deltav = {v}_{esc} - {v}_{orb} = \sqrt{\dfrac{2GM}{R}} - \sqrt{\dfrac{GM}{R}} = ( \sqrt{2} - 1 ) \sqrt{\dfrac{GM}{R}}$
$= ( \sqrt{2} - 1 ) \sqrt{gR}$
$= ( \sqrt{2} - 1 ) \sqrt{10 \times 6400 \times {10}^{3}}$
$= 8 ( \sqrt{2} - 1 ) km{s}^{- 1}$