# Velocity as a Vector

1. Jan 21, 2009

### Random-Hero-

1. The problem statement, all variables and given/known data

A light plane is traveling at 175km/h on a heading of N8°E in a 40km/h wind from N80°E. Determine the plane's ground velocity.

2. Relevant equations

3. The attempt at a solution

After I did all the graphing and trig. I came out with x^2 = 175^2 + 40^2 - 2(175)(40)cos108

which ends up being roughly 191.18, but the answer tells me its 167 km/h, N5°W

If anyone could help me out with this it would really be great, im having a rough time with it.

2. Jan 21, 2009

### phreak

Break it up into components: NS, EW. The direction NS is y = 175 sin(82) - 40 sin(10), where + is N. The direction EW is x = 175cos(82)-40cos(10), where + is E. To get their length, calculate $$D = \sqrt{x^2+y^2}$$. I'll leave the direction to you.

3. Jan 21, 2009

### Random-Hero-

Thanks a bunch! that helped tons!!