Finding the minimum time for crossing a river

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To find the minimum time for crossing a river, the swimmer's velocity relative to the ground must be directed at an angle to the current, allowing for perpendicular movement across the river. The time taken to cross can be expressed as a function of the angle of swimming. This approach involves calculating the swimmer's effective velocity and the distance between the banks. By optimizing the angle, the swimmer minimizes the crossing time despite the current's influence. Understanding these dynamics is crucial for solving the problem effectively.
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Homework Statement



Finding the minimum time for crossing a river[/B]


how is the minimum time crossed by distance between the banks/velocity of swimmer with respect to ground as mentioned in the video?

Homework Equations

The Attempt at a Solution


The minimum time is only possible when velocity of man with respect to ground is at angle to the current flow so that he moves perpendicular to the river flow
 
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The first thing to do in a problem like this is to write down an equation for the time as a function of the angle. Can you do that?
 

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