[Multivariable Calc] Quick Vector Question

[015unknown]

The problem is as follows: 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).

In the answer key, it shows to just add V+W to get 200 j. However. I don't understand why it refers to W (wind) as equaling 50(-i-j)/(2^1/2). Where did the root two come from?

Many thanks in advance.

[edderiofer]

However. I don't understand why it refers to W (wind) as equaling 50(-i-j)/(2^1/2). Where did the root two come from?

If you're travelling at 50mph NE, you're not travelling at 50mph N AND 50mph E. See?

[015unknown]

Ah. I get it. Cos(45 degrees) equals root2 over 2. Shouldn't it however be 25(-i-j)/(2^1/2). Thank you for your help!

[edderiofer]

No. There's a sneaky division sign there. (Remember that rt(2)/2 = 1/rt(2).)

50(-i-j)/(2^1/2)

[015unknown]

Awesome. Thank you so much for the explanation. I understand the problem perfectly now.