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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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