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Question

# A fish rising vertically with speed 3 m/s to the surface of water sees a bird diving vertically towards it with speed 9 m/s. Given aμw=(4/3). The actual velocity of dive of bird is

A
6 m/s
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B
4 m/s
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C
8.4 m/s
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D
4.5 m/s
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Solution

## The correct option is D 4.5 m/sGiven,Rateatwhichthefirstisrising=3m/sRateatwhichthekingfisherisdiving=9m/s]Refractiveindexofwater=43Ifatanyinstant,thefishisatadepth′x′belowwatersurfacewhile,thebirdisataheight′y′abovethesurface,thentheapparentheightofthebirdfromthesurfaceasseenbythefishwillbegivenbyμ=ApparentheightRealheightor,Apparentheight=μySo,thetotalapparentdistanceofthebirdasseenbythefishinwaterwillbeh=x+μyNow,differentiatingw.r.ttime,wegetdhdt=dxdt+μdydt⇒9=3+μ(dydt)⇒dydt=643=4.5m/sHence,option (D) is correct answer.

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