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Q.

A tank is filled upto a height 2H with a liquid and is placed on a platform of height H from the ground. The distance y (in m) from the ground where a small hole is made in the tank, to get the maximum horizontal range R is (take H = 1.5 m)

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answer is 2.25.

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Detailed Solution

$Velocity of efflux v = \sqrt{2 gh} = \sqrt{2 g (3 H - y)}$

Time of flight $\Rightarrow t = \sqrt{\frac{2 y}{g}}$

Range, $R = vt = 2 \sqrt{y (3 H - y)}$

R to be maximum, $\frac{dR}{d y} = 0$

on solving we get $y = \frac{3 H}{2} = \frac{3 (1.5)}{2} = 2.25 m$

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A tank is filled upto a height 2H with a liquid and is placed on a platform of height H from the ground. The distance y (in m) from the ground where a small hole is made in the tank, to get the maximum horizontal range R is (take H = 1.5 m)