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Q.

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging stream of water strikes the ground at the maximum range is __________ m.

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answer is 6.

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Detailed Solution

Question Image

From the figure,

The water jet's range is,

$R = v \times t = \sqrt{2 gh} \times \sqrt{(12 - h) 2 g} = \sqrt{4 h (12 - h)}$

In the case of maximum range, R

$\frac{dR}{dh} = 0$

$\frac{d (\sqrt{48 h - 4 h^{2}})}{dh} = (24 - 4 h) \sqrt{48 h - 4 h^{2}} = 0$

$h = 6 m$

Hence the correct answer is 6m.

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The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging stream of water strikes the ground at the maximum range is __________ m.