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Q.

A river is flowing due east with a speed $3 m s^{- 1}$ . A swimmer can swim in still water at a speed of $4 m s^{- 1}$ . If swimmer starts swimming due north, then the magnitude of resultant velocity of the swimmer is

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a

$3 m s^{- 1}$

b

$5 m s^{- 1}$

c

$7 m s^{- 1}$

d

$2 m s^{- 1}$

answer is B.

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Detailed Solution

A river is flowing due east with a speed 3 ms-1. A swimmer c

Here, Velocity of water flowing in river, $v_{r} = 3 m s^{- 1}$

Velocity of swimmer in still water, $v_{s} = 4 m s^{- 1}$

From figure, The resultant velocity of the swimmer is

$|v| = \sqrt{v_{s}^{2} + v_{r}^{2}} = \sqrt{(4)^{2} + (3)^{2}} = \sqrt{25} = 5 m s^{- 1}$

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A river is flowing due east with a speed 3ms-1. A swimmer can swim in still water at a speed of 4ms-1. If swimmer starts swimming due north, then the magnitude of resultant velocity of the swimmer is