Question

Water stands at a height H in a tall cylinder (see figure). Two holes A and B are made on the sides of the cylinder. If hole A is at a height $h$ above the ground, what is the height of hole B above the ground so that the two streams of water emerging from holes A and B strikes the ground at the same point?

Answer 1

Given,

Water stands at a height $=H$

Solution

ranges are same then two holes $\left(1\right)h$ above

Let, t is time taken by the jet to travel the vertical height $H$ from bottom of the cylinder and $v$ is the velocity steam of steam of water.

$H=\frac{1}{2}g{t}^2\to \left(1\right)t=\sqrt{\frac{2H}{g}}\to \left(2\right)v=\sqrt{2gh}\to \left(3\right)$

The horizontal distance R travelled by stream

$V_t=\frac{(2gh{)}^{1/2}}{(2gH{)}^{1/2}}\to \left(4\right)$

Solving equation $\left(4\right)$ we get $h$ (depth of water in the cylinder)$=\frac{R^2}{4H}$

R be the radius of the hole of B.