Question

A water barrel stands ona table of heighth. lf a small hole is punched in the side of the barrel at its base, it is found that the resultant stream of water strikes the ground at a horizontal distance R from the barrel.What is the depth of water in the barrel?

Answer 1

Let the depth of water in the barrel be $H$.

$\therefore$ Velocity of water coming out of the barrel $v=\sqrt{2gH}$

Also the horizontal range where the water strikes the ground $R=v\times \sqrt{\frac{2h}{g}}$

$\therefore$ $R=\sqrt{2gH}\times \sqrt{\frac{2h}{g}}$

OR $R^2=4hH$ $⟹$ $H=\frac{R^2}{4h}$