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@Gyro Gearloose
Note for OP
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Vr is velocity of river. Vs is velocity of swimmer . i figured velocity perpendicular to AC should be zero.
if Vs acts at some random angle alpha then Vsr ( Vel of swimmer wrt r ) = Vs cosalpha , the velocity which drives the swimmer along that line
therefore Vssinalpha = Vrcostheta
+solved @vj25_
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