science
posted by liam on .
An aircraft travels through the air with a velocity of 200m/s due east. It is found to be travelling over the ground with a velocity of 220m/s in a direction of 20(degree) south of east.The difference between the two is due to thw wind velocity.
What is the wind velocity?

draw the figure. For wind speed, use the law of cosines:
speed^2=200^2+220^22*200*220Cos20
make certain from your diagram you understand that.
Now, the hard part, the direction. Label the diagram, ABC, where A is at the origin, and you go CLOCKWISE around the triangle. You need angle B or C, then convert that to axis angles.
Lets do angle B.
Law of sines:
220/sinB=windspeedabove/sin20
solve for angle B. Now, that is the angle in the triangle. The direction then is, since it is measured against an axis, the direction is 90B South of East. Check that carefully.