Explanation

(b) By the law of conservation of energy
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {(U + K)}_{surface} = {(U + K)}_{\infty}$
$\Longrightarrow \ \ - \frac{GMm}{R} + \frac{1}{2}m{(3v_{e})}^{2} = 0 + \frac{1}{2}mv^{2}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - \frac{GM}{R} + \frac{9v_{e}^{2}}{2} = \frac{1}{2}v^{2}$
$Since,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{e}^{2} = \frac{2GM}{R}$
$\therefore\ \ \ - \frac{v_{e}^{2}}{2} + \frac{9v_{e}^{2}}{2} = \frac{1}{2}v^{2} \Longrightarrow v^{2} = 8v_{e}^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = 2\sqrt{2}v_{e}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2\sqrt{2} \times 11.2 = 31.7{kms}^{- 1}$