Question

An airplane flies horizontally from east to west at 280280 ​mi/hr relative to the air. if it flies in a steady 3030 ​mi/hr wind that blows horizontally toward the southwest ​(45degrees° south of​ west), find the speed and direction of the airplane relative to the ground.

Answer 1

We can find for the new speed of the plane using the cosine law. Let us say that the new speed is c:

c^2 = 280^2 + 30^2 – 2(280)(30) cos (90°+45°)

c = 302 mi/hr

The angle relative to the ground is calculated using sine law:

sin C / 30 = sin (90+45) / 302

C = 4.03°

The new speed is 302 mi/hr at -4.03° relative to the ground.