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Q.

To cross the river in shortest distance, a swimmer should swim making angle  with the upstream. What is the ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance. [Assume speed of swimmer in still water is greater than the speed of river flow

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a

$t a n θ$

b

$c o s θ$

c

$c o t θ$

d

$s i n θ$

answer is B.

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Detailed Solution

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Shortest time $t_{1} = \frac{d}{U}$ , shortest path $t_{2} = \frac{d}{U \cos (θ - 90)}$

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To cross the river in shortest distance, a swimmer should swim making angle  with the upstream. What is the ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance. [Assume speed of swimmer in still water is greater than the speed of river flow