Question

# Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel?

A

H/4

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B

H/2

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C

H/2

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D

H/3

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Solution

## The correct option is C H/2 Let the hole is made at a height 'h' above the bottom. Let the water spurts out through the hole with velocity 'v'. By Torricelli's equation v=√2g(H−h) Time taken by this get to reach the bottom, h=12gt2 ⇒t=√2hg Now horizontal distance covered by stream of water in this time interval, x=(√2g(H−h))x√2hg x=√2h(H−h) Maximizing x is same as maximizing x2 as it is the distance. d(x2)dh=2H−4h=0 H=H2

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