Q.

A swimmer crosses a flowing stream of width W to and fro in time t1. The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2W in still water, then

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a

t22 = t1t3

b

t3 = t1+t2

c

t32 =t1t2

d

t12 = t2t3

answer is A.

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Detailed Solution

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Let v be the river velocity and u the velocity of swimmer in still water. Then

t1 = 2(Wu2-v2)

t2 = Wu+v+Wu-v = 2uW u2-v2 and t3 = 2Wu

Now we can see that t12 = t2t3

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A swimmer crosses a flowing stream of width W to and fro in time t1. The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2W in still water, then