The speed of a boat is 5 km/h in still water. It crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water is
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The swimmer must swim as shown
\(v = \frac{5}{60} \text{ km/min}\)
\(15 = \frac{1}{v \sin \theta} \text{ or } v \sin \theta = \frac{1}{15}\)
\(\text{or } \frac{5}{60} \sin \theta = \frac{1}{15}\)
\(\therefore \sin \theta = \frac{4}{5}\)
\(\cos \theta = \frac{3}{5} \text{ and } u = v \cos \theta\)
\(= \frac{5}{60} \times \frac{3}{5} = \frac{1}{20} \text{ km/min} = 3 \text{ km/h}\)
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