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  • A fish in an aquarium approaches the left wall at a rate of <img alt="2.5 \mathrm{~m} / \mathrm{s}" src="https://entrancecorner.oncodecogs.com/gif.latex?2.5%20%5Cmathrm%7B%7Em%7D%20/%20%5Cmathrm%7B

A fish in an aquarium approaches the left wall at a rate of 2.5 \mathrm{~m} / \mathrm{s} observes a fly approaching it at 8 \mathrm{~m} / \mathrm{s}.  If the refractive index of water is (4 / 3), find the actual velocity of the fly.

 

Option: 1

2.5 \mathrm{~m} / \mathrm{s}


Option: 2

3 \mathrm{~m} / \mathrm{s}


Option: 3

3.5 \mathrm{~m} / \mathrm{s}


Option: 4

3.75 \mathrm{~m} / \mathrm{s}


Answers (1)

best_answer

For the fish the apparent distance of the fly from the wall of the aquarium is \mu \mathrm{x}, if \mathrm{x} is actual distance.

Then apparent velocity will be \frac{\mathrm{d}(\mu \mathrm{x})}{\mathrm{dt}}

\mathrm{\left(V_{\text {app }}\right)_{\text {fly }}=\mu V_{\text {fly }}}

Now the fish observes the velocity of the fly to be \mathrm{8 \mathrm{~m} / \mathrm{s}}
\mathrm{\Rightarrow} apparent relative velocity will be \mathrm{=8 \mathrm{~m} / \mathrm{s}}

\mathrm{\mathrm{V}_{\text {fish }}+\left(\mathrm{V}_{\text {app }}\right)_{\text {fly }}=8 \mathrm{~m} / \mathrm{s}}
\mathrm{\Rightarrow 3+\mu \mathrm{V}_{\mathrm{fly}}=8}
\mathrm{\mathrm{V}_{\mathrm{fly}}=5 \times \frac{3}{7}=3.75 \mathrm{~m} / \mathrm{s}}

Posted by

Rakesh

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