Show that moon would depart forever if its speed were increased by 42%

Expression for orbital velocity:
$v_0=\sqrt{\frac{GM}{R}}$

Expression for Escape velocity:
$v_e=\sqrt{\frac{2GM}{r}}$

From, the above expressions, it is clear that $v_e=\sqrt{2}{v}_o$

Escape velocity: It is the velocity required by moon to escape or depart forever.

Percentage increase of velocity required to reach terminal velocity.

$Percentage oincrea\sin = \left(\frac{v_e-v_0}{v_0}\right)$(100)

                                           $$\begin{gathered} =\left(\frac{\sqrt{2}{v}_0-v_o}{v_0}\right)\left(100\right) \\ =\left(\frac{1.414 v_0-v_0}{v_0}\right)100 \\ =41.4\% \end{gathered}$$

Hence, it is proved that  moon would depart forever if its speed were raised by 42%.