Question

An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel as shown in the figure. The water which comes out from the hole at the instant when hole is at height H above the ground, strikes the ground at a distance of x from P.

Answer 1

The vessel is falling under gravity. So the pressure at all point within the liquid remains same as the atmospheric pressure.

Using Bernoulli theorem, near the hole, for both inside and outside

$P_{inside}+\frac{{\rho v^2}_{outside}}{2}+\rho gh=P_{outside}$ [Here P is the atmospheric pressure]

Hence there is no water comes out of the vessel.