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Question

A fish is rising up vertically inside a pond with velocity 4 cm/s, and notices a bird, which is diving downward and its velocity appears to be 16 cm/s (to the fish). The real velocity of the diving bird is [μwater=4/3]

A
9 cm/s
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B
12 cm/s
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C
6 cm/s
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D
15 cm/s
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Solution

The correct option is A 9 cm/s
Given:
dydt=4 cm/s

Distance of bird as observed by fish,

z=y+μx=y+43x [ μ=happhreal]

differentiating both side w.r.t t, we get

dzdt=dydt+μdxdt

As the distances are decreasing, thus

dzdt=dydtμdxdt

16=443dxdt

dxdt=12×34=9 cm/s

So, the real velocity of the diving bird is 9 cm/s.

Therefore, (a) is the correct option.

Why this question ?This question test the skill of instantaneousspeed and apparent speed.

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