# Relative velocity question - plane and wind

1. Oct 2, 2006

### maskd

Relative velocity question -- plane and wind

The distance between two cities A and B is l. An airplane travels back and forth between A and B, flying in a line, with velocity V relative to the air. (a) Find the total flight time, if the wind blows with velocity v, in a direction that forms an angle $$\Theta$$ with the direction AB. Does this time depends on the direction where the wind blows? (b) Show that the whole travel is only possible if v < V, and find the relation between the flight time when the wind blows in the direction AB and the time when it blows in the perpendicular direction; (c) Show that, whatever the direction of the wind is, it always turns the travel duration longer.

Note: the original question is in another language -- I tried to make the translation as accurate as possible.

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