I'm stuck on how to work out 1A-6 from problem set 1. I had worked the problem but my answer is completely wrong. How should I go about answering this: 1A-6 A small plane wishes to fly due north at 200 mph (as seen from the ground), in a wind blowing from the northeast at 50 mph. Tell with what vector velocity in the air it should travel (give the i j -components)

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I'm stuck on how to work out 1A-6 from problem set 1. I had worked the problem but my answer is completely wrong. How should I go about answering this: 1A-6 A small plane wishes to fly due north at 200 mph (as seen from the ground), in a wind blowing from the northeast at 50 mph. Tell with what vector velocity in the air it should travel (give the i j -components)

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I thought about it like this: So the 200 mph north vector is the sum of the 50mph northeast vector and some other vector that the plane is supposed to fly. I know that the north vector should have the components 0i+200j So first i find the i and j components of that 50mph vector. I draw my right triangle with an angle of 45 degrees (northeast). I find its i and j components using trig So the sum of the i components of the 50 vector and the plane vector should be 0. and the sum of the j components of the 50 vector and the plane vector should be 200.
I don't know if you have a solution for this, but I'll give mine. The components of the northeast vector are \[25\sqrt{2} i+ 25\sqrt{2}j\] from trig. The rest you should be able to make sense out of. The W E components need to cancel out like you said, and the N S component will add up to 200. So... \[25\sqrt{2} i+(200-25\sqrt{2})j\] Good?
My bad it's from the north east, so 25sqrt2 is added not subtracted from the N S component. An I noticed this is from a month ago, of course meaning this was somewhat pointless. So be it.

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Other answers:

since desired velocity is <0,200>, and wind is <-25rt(2), -25rt(2)>, plane's starting velocity, for desired resulting, must be <25rt(2), 200+25rt(2)>
How do you set up the triangle for the wind?

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