Airplane Flying: Finding Direction & Ground Speed

[pebbles]

Homework Statement

An airplane is flying toward the Southeast with a speed of 200 m/s, and the wind is blowing toward the Northeast with a speed of 60 m/s.
A. Which direction will the plane head now?
B. What is the groud speed of the plane?

Homework Equations

The Attempt at a Solution

I thought that the ground speed was determined by the vector of the wind and the plane, but I can't figure out how to find the direction... I thought about taking the arctan of the two values I was given, but I didn't think that would work because I did not know which should be the x and y values, and they are going different directions. Can anyone explain to me how to set this problem up?

 

[drpizza]

Since you've mentioned x and y values, I'd suggest setting up a coordinate system on your piece of paper (most people use top edge for North, left side for West, etc.) Then draw each vector in the proper direction. Now, if you make each vector a right triangle, it should be apparent which is the x and which is the y component (or components of E,W,N,and/or S)

 

[pebbles]

hm..I'm still confused. I keep staring at the problem!

:S

here's what i drew on my paper:

 

[Precursor]

Connect the tail of your wind vector with the tip of your plane vector. This will make a right angle triangle. Now, you can use the pythagorean theorem, and come up with the resultant vector (hypotenuse) which will be the plane's ground speed. You can then find the angle of the plane's heading, by placing theta between the tail of your resultant vector and the tail of your wind vector, and using SOH CAH TOA to solve for your angle.