Question

Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel figure ?

Answer 1

The velocity with which water will come out,

$\therefore v=\sqrt{2g(H-h)}$

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

= times of flight

$\therefore x=v\times t$

= $\sqrt{2g(H-h)}\times \sqrt{\frac{2h}{g}}$

= $\sqrt{4(Hh-h^2)}$

For x to be maximum,

$\frac{d}{dh}(Hh-h^2)=0$

$\Rightarrow 0=H-2h$

$\Rightarrow h=\frac{H}{2}$