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Question

# A tank with vertical walls is mounted so that its base is at a height H above the horizontal ground. The tank is filled with water to a depth 'h' . A hole is punched in the side wall of the tank at a depth ' x ' below the water surface. To have maximum range of the emerging stream,the value of x is

A
H+h4
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B
H+h2
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C
H+h3
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D
3(H+h)4
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Solution

## The correct option is A H+h2Horizontal velocity of ejection, when a vessel is filled with water to height h is √2gh∴ velocity of ejection =√2g(h−x)Time taken will be √2hg=√2(H+h−x)g∴range=2√(h−x)(H+h−x)[∵R=ut]range is max , when dRdx=0 ⇒x=H+h2

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