Question

A water barrel stands on a table of height $h$. If 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 table. What is the depth of water in the barrel?

• A. $\frac{R^2}{h}$
• B. $\frac{R^2}{2h}$
• C. $\frac{R^2}{4h}$
• D. $\frac{4R^2}{h}$

Answer 1

Answer: (C)

From Torricelli’s theorem
$v=\sqrt{2gd}\dots \left(i\right)$
where $v$ is horizontal velocity and $d$ is the depth of waterin barrel
Time $t$ to hit the ground is given by
$h=\frac{1}{2}g{t}^2$ or $t=\sqrt{\frac{2h}{g}}$
$\therefore R=vt=\sqrt{\left(2gd\right)}\sqrt{\frac{2h}{g}}=2\sqrt{dh}$ (Using (i))
$\therefore R^2=4dh$ or $d=\frac{R^2}{4h}$