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Q.

A river is flowing with a speed of 1km/ h . A swimmer wants to go to point ‘C’ starting from ‘A’. He swims with a speed of 5km/ h , at an angle $θ$ , w.r.t t river. If AB = BC = 400m. Then

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a

Time taken by the man is 8min

b

The value of $θ$ is 45⁰

c

The value of $θ$ is 53⁰

d

Time taken by the man is 6min

answer is A, B.

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Detailed Solution

$\begin{array}{l} V_{M} = (1 + 5 \cos θ) \hat{i} + 5 \sin θ \hat{j} \\ Drift = (1 + 5 \cos θ) \frac{0 .4}{5 \sin θ} = 0 .4 \\ \Rightarrow 1 + 5 \cos θ = 5 \sin θ \\ \Rightarrow 5 (\sin θ - \cos θ) = 1 \Rightarrow θ = 53^{0} \\ Time = \frac{0 .4}{5 (\frac{4}{5})} = 0 .1 h = 6 \min \end{array}$

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