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Question
A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river.
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Solution
Given:
Width of the river = 500 m
Rate of flow of the river = 5 km/h
Swimmer's speed with respect to water = 3 km/h
As per the question, the swimmer heads in a direction making an angle θ with the flow.
We know that the vertical component of velocity 3 sin θ takes him to the opposite side of the river.
Distance to be travelled = 0.5 km
Vertical component of velocity = 3 sin θ km/h
Thus, we have:
\[\text{ Time }= \frac{\text{ Distance } }{\text{ Velocity }} = \frac{0 . 5}{3\sin\theta} h = \frac{500 \times 6}{5\sin\theta} = \frac{600}{\sin\theta} s\]
∴ Required time =\[\frac{10 \text{ minutes } }{\sin\theta}\]
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