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Relative Velocity in 2D

WIND IS BLOWI...

Question

WIND IS BLOWING WEST TO EAST ALONG 2 PARALLEL TRACKS, 2 TRAINS MOVING WITH THE SAME SPEEDIN OPP DIRECTIONS ON THESE TRACKS HAVE THE STEAM TRACKS,IF 1 STEAM TRACK IS DOUBLE THAN THE OTHER, WHAT IS THE SPEED OF EACH TRAIN?

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Solution

Let v be the velocity of the train and w be the velocity of wind.
Relative velocity of train A with respect to wind = v + w
Relative velocity of train B with respect to wind = v - w
v + w = 2(v - w)
Therefore, v = 3w.
Velocity of each train is three times the velocity of wind.

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