You are on an airplane traveling 30° south of due west at 140 m/s with respect to the air. The air is moving with a speed 35 m/s with respect to the ground due north.

1) What is the speed of the plane with respect to the ground?

2) What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due easth).

3) How far west will the plane travel in 1 hour?

1) By the Cosine Law:

v² = 140² + 35² - 2 · 140 · 35 · cos 60°

v² = 19,600 + 1,225 - 2 · 4,900 · 1/2 = 15,925

v = √15,925

v = 126.2 m/s

2) By the Sine Law:

126.2 / sin 60° = 35 / sin x

126.2 / 0.866 = 35/sin x

sin x = 0.24

x = sin^ (-1) 0.24 = 13.9°

α = 30° - 13.9° = 16.1°

The heading of the plane (270° represents due West):

270° - 16.1° = 253.9°

3) In 1 hour:

d = 126.2 m/s · 3600 s = 454,320 m

454,320 m · cos 16.1° = 454,320 m · 0.96 = 436,147.2 m