In a cylindrical water tank, there are two small holes $A$ and $B$ on the wall at a depth of $h_1$ , from the surface of water and at a height of $h_2$ from the bottom of water tank. Surface of water is at height of $h_2$ from the bottom of water tank. Surface of water is at heigh $H$ from the bottom of water tank. Water coming out from both holes strikes the ground at the same point $S$. Find the ratio of $h_1$ and $h_2$
AIEEE 2012, Diffcult
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Range is same for both holes
$\therefore \,2\sqrt {(H - {h_1}){h_1}} = 2\sqrt {\left( {H - {h_2}} \right){h_2}} $
Squaring both sides,
$4\left( {H - {h_1}} \right){h_1} = 4\left( {H - {h_2}} \right){h_2}$
$H{h_1} - h_1^2 = H{h_2} - h_2^2$
On solving we get,
$H = {h_1} + {h_2}$
Hence, the ratio of $\frac{{{h_1}}}{{{h_2}}}$ depends on $H$.
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