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  4. A river is flowing from east to west at a speed of 5 m / min. A man on south bank of river, capable of swimming 10 m / min in still water, wants to swim across the river in the shortest time. He should swim :-

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Q. A river is flowing from east to west at a speed of $5 \,m / min$. A man on south bank of river, capable of swimming $10\, m / min$ in still water, wants to swim across the river in the shortest time. He should swim :-

Solution:

image
$y: v \cos \theta t=d$
$t =\frac{ d }{ V \cos \theta}$
$t$ will be minimum, if $\cos \theta$ is maximum
$(\cos \theta)_{\max }=1 \Rightarrow \theta= t$
To cross the river in minimum time, the man should swim perpendicular to the river flow, i.e. due north.