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A stream of water coming out from a pipe at point A as shown in figure. A rod AD is along the projected velocity of stream. There are four points A,B,C,D on the rod (AB = BC = CD) from which string of length $l_{1}, l_{2}, l_{3}$ are hanging. These string are touching the trajectory of stream of water. If the length $l_{2} = 4 m$ find $l_{3}$

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Detailed Solution

$l_{2}' = 4 m$

$S = \frac{1}{2} \times g t^{2}$

$4 = \frac{1}{2} \times 10 t_{2}^{2}$

$t^{2} = \sqrt{0.8}$

$t_{1} : t_{2} : t_{3} = 1 : 2 : 3$

$t_{1} = \frac{1}{2} \sqrt{0.8}$

$t_{2} = \frac{\sqrt{0.8}}{\sqrt{0.8}}$

$t_{3} = \frac{3}{2} \sqrt{0.8}$

$l_{3} = \frac{1}{2} g t^{2} = \frac{1}{2} \times 10 \times \frac{9}{4} \times 0.8$

$l_{3} = 9 m$

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