Question

An airplane flies due south at 175km/h relative to the air. There is a wind blowing at 85 km/h to the east relative to the ground. What are the plane's speed and direction relative to the ground.

Answer 1

plane's speed is
v(plane) = sqrt(v(wind)^2 + v(relative to air)^2) = 194,55 km/h
direction: south-west with angle
arccos(85/194) = 1,12 rad = 63,27 grad from south