# Thread: Pilot and wind velocity vector help

1. ## Pilot and wind velocity vector help

A pilot needs to fly 35 degrees east of north. He's flying at a speed of 105 miles per hour at fixed altitude with no wind. When he reaches a point, he encounters wind with a velocity of 15 miles per hour in the direction 10 degrees east of north. Express the velocity of the wind W as a vector. Express the velocity of the airplane A as a vector.

I don't understand how to find the velocity and express that as a vector.

2. ## Re: Pilot and wind velocity vector help

A pilot needs to fly 35 degrees east of north. He's flying at a speed of 105 miles per hour at fixed altitude with no wind. When he reaches a point, he encounters wind with a velocity of 15 miles per hour in the direction 10 degrees east of north. Express the velocity of the wind W as a vector. Express the velocity of the airplane A as a vector.
Air vector is the motion of the aircraft moving relative to the air mass.

Wind vector is the motion of the air mass relative to the Earth's surface.

Ground Track vector is the motion of the aircraft relative to the Earth's surface.

Air vector + Wind vector = Ground Track Vector

Are you familiar with adding vectors using the method of components? ...

$\color{blue}{[105\cos(55)\vec{i} + 105\sin(55)\vec{j}]} + \color{red}{[15\cos(80)\vec{i} + 15\sin(80)\vec{j}]} = \color{green}{[105\cos(55)+15\cos(80)]\vec{i} + [105\sin(55)+15\sin(80)]\vec{j}}$

3. ## Re: Pilot and wind velocity vector help

I'm not familiar with the method of components. Where did you get the numbers 80 and 55 from?

Also the problem asks for (1) the velocity of the wind W as a Vector and (2) the velocity of the airplane A as a vector, so does that mean I shouldn't include the ground track vector?

The W and A have those arrows above them, I'm not sure how to format that correctly.

4. ## Re: Pilot and wind velocity vector help

ok, I'm confused ... you are given the speed and direction of the airplane with no wind (that is the air vector, btw) and the speed and direction of the wind, and you're asked to express both as a vector?

What format for expressing vectors have you been taught? Polar, rectangular, ... some other way?

5. ## Re: Pilot and wind velocity vector help

I'm sorry I'm so confusing! I don't know what format I've been taught. In my notes it all just has letters with arrows on top. Some of them are the letters 'i" and "j" where the dots have been replaced by upwards pointing arrows. If that doesn't make sense, I can PM you a picture of the problem. Thank you for trying at least.

6. ## Re: Pilot and wind velocity vector help

"i" & "j" is rectangular notation ... I expressed both the air vector and the wind vector using that notation in my initial post.

See the attached diagram to see where 55 and 80 degrees came from ...

7. ## Re: Pilot and wind velocity vector help

Oh that makes so much sense thank you very much!