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{4 R^{2}}{h} $

Answer 1

Answer: (C)

From Torricelli’s theorem
$ v=\sqrt{2gd} \ldots\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}gt^{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} $