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Discuss the motion of a swimmer who wants to cross a river in the shortest possible time. (i) Find the time of crossing, the river. (ii) The distance where the swimmer reaches opposite bank.

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Its about Law of vector addition. Velocity vector for the swimmer should be chosen such that its addition with the velocity vector of the river gives a resultant vector which is perpendicular to the velocity vector of river.
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A Retired Physics Teacher for NEET JEE, Board

One can cross the river in a shortest time, if one start swimming in a direction perpendicular to the river flow. Let U = Velocity of the swimmer perpendicular to the river flow. D= width of the river. T = time to cross the river. Vw= Velocity of the water. Hence T = ( D/U) S = Over carried...
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One can cross the river in a shortest time, if one start swimming in a direction perpendicular to the river flow. Let U = Velocity of the swimmer perpendicular to the river flow. D= width of the river. T = time to cross the river. Vw= Velocity of the water. Hence T = ( D/U) S = Over carried distance , on the opposite bank & this distance will be away from the directly opposite to the starting point. Where S = Vw×T = ( D / U) T units. read less
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