Question

Plane Ride
You are traveling on an airplane. The velocity of the plane with respect to the air is 110 m/s due east. The velocity of the air with respect to the ground is 43 m/s at an angle of 30° west of 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 east).° East of due North
3)How far east will the plane travel in 1 hour?

Answer 1

I'll show you what I think the answer is and how I got there: first I figured how far the wind would push the aircraft North and West relative to the ground: if the triangle looks like this then the westward component would be half of 43 or 21.5m/s (sine is opposite over hypotenuse and sin30 is 0.5). Cosine 30 is 0.866 so the northerly component will be 37.2. The plane will be heading east at 110 minus 21.5m/s and North at 37.2m/s. The angle relative to the ground will be the reverse tangent of 37.2/88.5 and the speed relative to the ground will be the square root of the sum of the squares: