Three swimmers can swim equally fast relative to the water. they have a race to see who can swim across a river in the least time. swimmer a swims perpendicular to the current and lands on the far shore downstream, because the current has swept him in that direction. swimmer b swims upstream at an angle to the current and lands on the far shore directly opposite the starting point. swimmer c swims downstream at an angle to the current in an attempt to take advantage of the current. who crosses the river in the least time?

Swimmer A crosses the river in the least time.

Explanation:

In the Question, current means the flow of the river. Downstream flow means flow in the direction of water flow and upstream flow means opposite to the direction of water flow.

Swimmer B swims upstream at an angle to the current and lands on the far shore directly opposite the starting point. As swimmer B swims upstream to the current, so one component of this velocity cancelled out by current and only one component of his velocity which is perpendicular to the current help him to cross the river.

Swimmer C swims downstream at an angle to the current in an attempt to take advantage of the current. As Swimmer B, the perpendicular component of velocity by Swimmer C help him to cross the river.  

Swimmer A swims perpendicular to the flow of the river but lands far shore downstream,  So it has two component of velocity one is perpendicular to the flow of the river which is by the swimmer and the other is parallel to the current due to the flow of the river.As velocity by the Swimmer A acts perpendicular to the current,

So, the whole of his velocity goes into crossing the river and nowhere else. But in case of Swimmer B and C, one component of their velocity waste and one component of their velocity help them to cross the river.  

So, Swimmer A crosses the river in the least time.

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