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Vectors in the Plane: Plane+Wind question

  1. Feb 25, 2007 #1
    1. The problem statement, all variables and given/known data
    An airplane has an airspeed of 430 mph at a bearing of S 45 degrees E. If the wind is 35 MPH in direction of N 30 degrees E, find groundspeed and direction of plane.

    2. Relevant equations
    [[v]]([cos theta], [sin theta])

    3. The attempt at a solution

    430(cos 315,sin315)+35(cos30,sin30)=?????<334.4,-286.6>

    Back of book says that the ground speed is 422.3.. and if i go the vector wrong, that means magnitude and direction will be wrong also.. Where did I go wrong?
  2. jcsd
  3. Feb 25, 2007 #2


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    Science Advisor

    If the numbers you give are correct, then you have it right. The ground speed is 440.3, not 422.3.
  4. Feb 25, 2007 #3
    Hope you're right. This isn't the 1st time the book has a typo or something.
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