An airplane flies with a velocity of 55.0 m/s [ 35° 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 [53° N of W], what was the wind velocity?

21 m/s.  

Explanation:

The computation of the wind velocity is shown below:

But before that, we need to find out the angles between the vectors

53° - 35° = 18°

Now we have to sqaure it i.e given below

v^2 = 55^2 + 40^2 - 2 · 55 · 40 · cos 18°

v^2 = 3025 + 1600 - 2 · 55 · 40 · 0.951

v^2 = 440.6

v = √440.6

v = 20.99

≈ 21 m/s

Hence, The wind velocity is 21 m/s.  

explanation:

wheres the pic