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A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one of the walls at a depth h below the surface of water. Express the horizontal distance X in terms of H and h.

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$X = \sqrt{h (H - h)}$

$X = \sqrt{\frac{h}{2} (H - h)}$

$X = 4 \sqrt{h (H - h)}$

$X = 2 \sqrt{h (H - h)}$

answer is C.

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Detailed Solution

Vertical distance covered by water before striking ground $= (H - h) .$

Time taken is, $t = \sqrt{2 (H - h) / g}$

Horizontal velocity of water coming out of hole at P, $u = \sqrt{2 g h}$

$∴$ Horizontal range $= u t = \sqrt{2 g h} \times \sqrt{2 (H - h) / g} = 2 \sqrt{h (H - h)}$

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