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May 5, 2016

# Homework Help: science

Posted by liam on Wednesday, October 10, 2012 at 7:32am.

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?
• science - bobpursley, Wednesday, October 10, 2012 at 8:09am

draw the figure. For wind speed, use the law of cosines:

speed^2=200^2+220^2-2*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 90-B South of East. Check that carefully.