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^{ }A SWIMMER SWIMS ACROSS A 2 KM WIDE RIVER BY KEEPING 150 DEGREE WITH FLOW OF RIVER. THE RIVER FLOWS WITH 2KM/H AND THE SPEED OF THE SWIMMER IN STILL WATER IS 3KM/H. FIND THE TIME HE TAKES TO CROSS THE RIVER.

PLS XPLAIN IN DETAIL WITH A DIAGRAM

Dear Student,

Please find below the solution to the asked query:

The situation is as shown in the figure.

Therefore, the velocity of the man parallel to the river flow makes him to move along the river or against the river. This will not support him to cross the river.

So, the velocity of the man perpendicular to the river makes him to cross the river. Which is,

$u\mathrm{cos}{30}^{0}=3\times \left(\frac{\sqrt{3}}{2}\right)\raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.$

So, the time taken by the person to cross the river is,

$t=\frac{d}{u\mathrm{cos}{30}^{0}}=\frac{2}{{\displaystyle \raisebox{1ex}{$3\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}=\frac{4}{3\sqrt{3}}=\frac{4}{5.2}\phantom{\rule{0ex}{0ex}}\Rightarrow t=0.692hrs\phantom{\rule{0ex}{0ex}}$

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