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A man is trying to cross a river flowing at a speed of $5 m s^{- 1}$ to have least possible displacement by swimming at an angle of $143 °$ to the stream. The drift he suffers when he is crossing the same river in least possible time is (width of river = 1km)______.

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$800 m$

$600 m$

$400 m$

$200 m$

answer is A.

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Detailed Solution

Case 1: $\sin 53^{0} = \frac{v_{R}}{v_{S R}}$
$\Rightarrow v_{S R} = \frac{25}{4} m / s$

Case 2:

$t = \frac{S}{v_{S R}} = \frac{1000}{25} \times 4 = 160 s$

$D r i f t = v_{R} t = 5 \times 160 = 800 m$

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