# Q.A man swims across a river with speed of 5km/hr( in still water), while a boat goes upstream with speed 12km/hr (in still water). How fast and in which direction does the man appear to go to the boatman? Given that speed of flowing water is 2km/hr.

1
by shr14

2015-05-03T13:47:38+05:30

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The man swims  perpendicular to the flow or velocity of river water.
speed of man = 5 kmph  wrt water
boat is going upstream , velocity wrt water = 12 kmph

velocity of water in the river = 2 kmph

The vector component of velocity of water downstream is added to both boatman and the swimmer.  When we find the relative velocity of the swimmer wrt boatman, that will be canceled.

relative velocity of swimmer wrt boatman
= velocity of swimmer -  velocity of boatman      (vector subtraction)

as angle between the two vectors is 90 deg,

magnitude of relative velocity =  √(5² + 12²)  = 13  kmph

direction:  at an angle of tan⁻¹ (12/5) to the flow of water.