A plane whose air speed is 200 km/h heads due North. But a 100 km/h northeast wind suddenly begins to blow. What is the resulting velocity of the plane with respect to the ground?

Answer 1

If by "northeast wind" you mean blowing in the NE direction, then the resultant vector
v = 200j + 50√2 i + 50√2 j
= 50√2 i + (200 + 50√2)j
|v| = 100√(5+2√2)
direction is N 14.64° E

Alter that if you meant blowing from the NE