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Question

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t north is given by :

A
$$30^o $$ west
B
$$0^o$$
C
$$60^o $$ west
D
$$45^o $$ west
Solution
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Correct option is A. $$30^o $$ west
$$V_{SR} = 20 m/s$$
$$V_{RG} = 10 m/s$$
$$\bar{V}_{SG} = \bar{V}_{SR} + \bar{V}_{RG}$$
So,
$$sin \theta = \dfrac{|\bar{V}_{RG}|}{|\bar{V}_{SR}|}$$
$$sin \theta = \dfrac{10}{20} $$
$$\implies sin \theta = \dfrac{1}{2}$$
$$\implies \theta = 30^o $$ west

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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t north is given by :
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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north, is given by
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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north, is given by
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Assertion
A river is flowing from east to west at a speed of $$5\ m/min$$. A man on the south bank of river, capable of swimming $$10\ m/min$$ in still water, wants to swim across the river in shortest time. He should swim due north.
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