Answer
$s=\dfrac{3}{4}H$
Work Step by Step
Use velocity-time equation.
$v=u+at$
This implies
$t=\frac{u}{g}$ [ v=0] ...(1)
Use position-time equation.
$s=ut+\dfrac{1}{2}gt^2$
From equation (1), we have
$s=u(\frac{u}{g})+\dfrac{1}{2}g(\frac{u}{g})^2$
$s=\dfrac{u^2}{2g}=H$ ...(2)
Also,
$s=u \cdot (\dfrac{u}{2g})-\frac{g}{2}(\dfrac{u}{2g})^2$
This implies
$s=\dfrac{3}{4}H$
