$\Rightarrow \quad u=\sqrt{\frac{2 h}{g}} \times g=\sqrt{2 g h}$

$\therefore \quad t_{1}=$time to reach top $=\frac{u}{g}=\sqrt{\frac{2 h}{g}}$

$\therefore \quad H=h+h^{\prime}=2 h$

$t_{2}=$ time of fall $=\sqrt{\frac{2 \times(2 h)}{g}}$

$\quad=2 \sqrt{\frac{h}{g}}$

Total time $=t_{1}+t_{2}$

$\quad=(2+\sqrt{2}) \sqrt{\frac{h}{g}}$

$\quad=3.4 \sqrt{\frac{h}{g}}$