Question

An airplane flies with a velocity of 55.0 m/s [35o N of W] with respect to the air (this is known as air speed). If the velocity of the airplane according to an observer on the ground is 40.0 m/s [53o N of W], what was the wind velocity?

Answer 1

v - the wind velocity;
53° - 35° = 18°
v² = 55² + 40² - 2 · 55 · 40 · cos 18°
v² = 3025 + 1600 - 2 · 55 · 40 · 0.951
v² = 440.6
v = √440.6
v = 20.99 ≈ 21 m/s
Answer: The wind velocity is 21 m/s.