A swimmer crosses the river along the line making an angle of 45° with the direction of flow. velocity of the river water is 5 m/sec Swimmer takes 6 seconds to cross the river of width 60 metre find the velocity of the swimmer with respect to water .

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Solution

Let the river flow along y direction with a velocity of 5 j m/s.
Let the swimmer crossover along the vector: i + j (at 45°)
displacement of swimmer just after crossing = 60 i + 60 j meters

The speed of swimmer wrt to stationary observer
= (60 i + 60 j) / 6 m/s = 10 i + 10 j m/s

velocity of swimmer relative to the river = 10 i + 10 j - 5 j
= 10 i + 5 j m/s

magnitude of velocity relative to river = 5√5 m/s

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