Question

As shown in the figure, water squirts horizontally out of two small holes in the side of the cylinder and the two streams strike the ground at the same point. If the hole $Q$ is at a height $h$ above the ground and the level of water stands at height $H$ above the ground, then the height of $P$ above ground level is

• A. $2h$
• B. $H/h$
• C. $H-h$
• D. $H/2$

Answer 1

Answer: (C)

$H-h$

For point $Q,x=2\sqrt{(H-h)h}$
For point $P,x=2\sqrt{h^{\prime }(H-h^{\prime })}$
where $x=$ horizontal range of water.
$\therefore 2\sqrt{h(H-h)}=2\sqrt{h^{\prime }(H-h^{\prime })}$
$h(H-h)=h^{\prime }(H-h^{\prime })$
or $h^{\prime 2}-h^{\prime }H+h(H-h)=0$
Solving it, we get, $h^{\prime }=(H-h)$.