A jet airliner moving at 500 mph due east moves into a region where the wind is blowing at 120 mph in a direction north . What is the new velocity and direction of the aircraft?

Answer 1

Perform a vector addition
500 i + 120 j has a magnitude of
sqrt(500^2 + 120^2) = 514.2 mph
The ration of east and north components tells you the tangent of the direction.