A plane is headed east with an air speed of 294.0 m/s. The wind blows southeast at 42.0 m/s. Find the velocity of the plane relative to the earth.
I will assume that the wind blows toward the southeast, not from the southeast. Its velocity components are therefore 29.7 m/s south and 29.7 m/s east.
Add the wind speed vector and the planes air speed vector to get the ground speed vector, V. its components ate
Vx = 294 + 29.7 (east)
Vy = 29.7 (south)