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Question

There are two holes $$O_{1}$$ and $$O_{2}$$ in a tank of height H. The water emerging from $$O_{1}$$ and $$O_{2}$$ strikes the ground at the same points,as shown in fig. Then:
24416_5e632ffe11784e7db0ff6e0c0e59e089.png


A
H=h1+h2
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B
H=h2h1
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C
H=h1h2
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D
H=h2/h1
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Solution

The correct option is A $$H=h_{1}+h_{2}$$
At any height h below the surface , velocity of ejection $$ V = \sqrt{2gh}$$
time of flight $$t = \sqrt{2g (H-h)}$$ 
$$\therefore$$ Range $$R = vt = 2\sqrt{h (H-h)}$$ 
If $$ R_{1} = R_{2} \Rightarrow h_{1}(H-h_{1}) = h_{2} (H-h_{2})$$ 
$$ \Rightarrow h_{1} = H-h_{2}$$ 
$$h_{1}+h_{2} =H$$

Physics

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