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Standard XII

Physics

Relative Velocity

A swimmer swi...

Question

A swimmer swims in still water at a speed of $5 k m / h r$ . He enters a $200 m$ wide river, having a river flow speed of $4 k m / h r$ . He proceeds to swim at an angle of $127^{\circ}$ with the river flow direction. He reaches directly opposite to the starting point and then swims with the river flow to cover a distance of $200 m$ . The total time taken by the swimmer to complete his journey is

5 m i n

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4 m i n

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3 m i n

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6 m i n

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Solution

The correct option is D $6 m i n$
Given, width of the river $d = 200 m$
velocity of the river $V_{r} = 4 k m / h r$
and, velocity of swimmer in still water $V_{s r} = 5 k m / h r$

As per the question, time taken by swimmer to reach directly opposite side is
$t_{1} = \frac{d}{5 c o s 37^{\circ}} = \frac{0.2}{4} h r = 3 m i n$
Also, the swimmer swims with the river flow to cover the distance $200 m$ , time taken by him for this is
$t_{2} = \frac{0.2}{4} h r = 3 m i n$
Thus, total journey time is $t_{1} + t_{2} = 6 m i n$

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