Question

A swimmer crosses the river along the line making an angle 45 degree with the direction of flow of river. if velocity of river is 5m/s and time taken by him is 6 seconds to cross width of river 60m. then find the velocity of swimmer w.r.t. to river

Answer 1

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

Answer 2

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