a twin-engine cessna is heading on bearing of 35 degrees with an air speed of 180 mph. if the wind is out with a bearing of 90 degrees at 40 mph, then what is the bearing of this course? what is the ground seed of the airplane?

Answer 1

vehicles and winds travel on a heading, not a bearing. Sadly, this distinction is ignored or unknown to many textbook writers and teachers.

But on to the math.

the Cessna in still air travels be at
(180 sin35°,180 cos35°) = (103.24,147.45)
The wind blows it an additional (-90,0)

Thus, its final velocity is (13.24,147.45)

Thus, its ground speed is √(13.24^2 + 147.45^2) = 148.04

and its heading is 5.2°