# Geometry/Discrete Math Velocity Vectors Help

I'm working on this problem and it's frustrated me and I was wondering if I could get a spot of help on it:

An airplane heads due south with an air speed of 480km/h. Measurements made from the ground indicate that the plane's ground speed is 528 km/h is 528 km/h at 15 degrees east of south. Calculate the wind speed.

I have a diagram of what I worked out so maybe someone could show me what I did right and what I did wrong, that'd be nice.

http://img497.imageshack.us/img497/6442/diag0ia.png [Broken]

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Fermat
Homework Helper
You've got your plane heading 15 deg south of east, not 15 deg east of south!
15 deg east of south is at -75 degrees( that's 75 degrees clockwise from direction of the positive x-axis)

Okay thanks. I'll try it again and see what I come up with.

Astronuc
Staff Emeritus
I would suggest using -j (-y) for S, and i (+x) for E.

Consider the ground speed as the true speed. Resolve the ground speed vector into its S and E components. The air speed is 480 km/h, so the air must have a southward component to carry the plane with a faster ground speed.

What are the S and E components of the ground speed vector?

I figured it out. The problem were in the angles, so I redrew it like this:

http://img490.imageshack.us/img490/842/diag3tf.png [Broken]

Then I used cosine law to get the wind speed. Just thought I'd post the solution so people would know :D

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