find the air velocity of a plane that must have a relative ground velocity of 250 km/h north if it encounters a wind pushing it toward the northeast at 75 km/h

Answer 1

Wind velocity vector + Air velocity vector = Ground velocity vector

Writing that as a vector equation:

75 cos 45 i + 75 sin 45 j + Vx i + Vy j = 250 j
Vx = -53.03 km/h
Vy = 250 - 53.03 = 196.97 km/h

i and j denote unit vectors in the east and north directions.

Vx and Vy are the x (east) and y (north) components of the required air velocity.

The required air speed is just 203.98 km/h