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Homework Help: Question on vector algebra

  1. Mar 10, 2012 #1


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    1. An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km (S 5° E) of Barrie. If the wind is blowing from the South with a velocity of 62 km/h, and the plane's air speed is 375 km/h, what direction must the pilot fly to make it to Toronto?

    2. Let u=<u_{1},u_{2}>, v=<v_{1},v_{2}> be vectors and let k be a scalar. Then u+v=<u_{1}+v_{1},u_{2}+v_{2}> and ku=<ku_{1},ku_{2}>.

    ||u|| = √(u^{2}_{1}+u^{2}_{2})

    u = ||u||(cos θ)i + ||u||(sin θ)j

    tan θ = sin θ / cos θ

    3. I tried vector addition but I'm just stumped (my cousin is taking a high school calculus course, and I volunteered to help him out).
    Last edited: Mar 10, 2012
  2. jcsd
  3. Mar 10, 2012 #2


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    It looks like you are just listing random formulas. :frown:

    I'll help you set it up since you are helping someone else. Call the wind vector ##\vec W = \langle 0,62\rangle##. Let ##\theta## be the polar coordinate (unknown) angle the plane flies, so the plane vector is ##\vec P = \langle 375\cos\theta,375\sin\theta\rangle##. You want the resultant vector for the plane and wind to be in the direction of the town, say ##\vec D = \langle \cos(-85^\circ),\sin(-85^\circ)\rangle##. So set up the equations ##\vec P + \vec W = k\vec D## and use the two component equations to solve for ##\theta##.
  4. Mar 10, 2012 #3


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    Hi LCKurtz,

    Thanks for all your help! As far as listing formulas, I was looking at all relevant formulas from my cousin's algebra textbook -- as a professional statistician, I admit to being rather embarrassed that I had trouble with this question! :redface:
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