Answer
$(a)\space\frac{V^{2}}{2h}$
$(b)\space \frac{2h}{V}$
Work Step by Step
Please see the attached image first.
Let's apply equation $V^{2}=U^{2}+ 2aS$ to find the acceleration.
$\uparrow V^{2}=U^{2}+ 2aS$
Let's plug known values into this equation.
$V^{2}=(0)^{2}+2ah$
$\frac{V^{2}}{2h}= a\space (Acceleration\space of\space the \space rocket)$
(b) Let's apply equation $V=U+ at$ to find the time taken to reach the height h.
$\uparrow V=U+at$
Let's plug known values into this equation.
$V=0+(\frac{V^{2}}{2h})t$
$\frac{2h}{V}=t\space (Time\space taken)$
