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This cannot be calculated without knowing the aerodynamics of the plane. Since air is fluid, it is capible of going around the plane, and will not nessicarily move the plane 50 mph E.

If the wind holds steady (as in, not a single gust but a continuous wind) it will eventually push the plane up to 50 mph E.

At that time the pane will have a speed of 403.14 mph going 82.875 degrees (with 90 degrees being due north).

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Q: A plane is movine north at 400 mph and a wind suddenly blows from west to east at 50 mph What is the plane's new velocity and direction?
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