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An airplane in the wind

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data

    An airplane is traveling at 30 m/s and wishes to travel to a point 8000 m NE (45 degrees). If there is a constant 10m/s wind blowing west:
    A) In what direction must the pilot aim the plane in degrees?
    B) How long will the trip take?

    2. Relevant equations

    Basic kinematic equations and trigonometry.

    3. The attempt at a solution

    Since I know only the magnitude of the velocity vector, and have to find the direction, I'm having trouble.

    I've tried taking the arcsin of 10/30 (Opposite over Hypotenuse) and got 19.47 degrees. Using the Law of Sines, I can calculate the other angles and the other side length.

    Side Length (m/s) Angle (Degrees)
    10 19.47
    30 58.4
    29.33 102

    Obviously, the 102 degrees doesn't make sense, since it is not opposite the largest side.

    Am I making this much more difficult than it really is?

    Please advise.
  2. jcsd
  3. Oct 14, 2008 #2


    User Avatar
    Homework Helper

    Likely you aren't making it difficult enough.

    What you do have is a vector addition. Except this one involves certain variables. I would recommend that you construct the vectors and their components, and then add them as you know they must be added to end at your destination.

    For instance let A be your wind speed blowing West. Withe East being positive X and H being the time to get there:

    [tex] \vec{A} = -10*H*\hat{x} [/tex]

    Likewise for the Plane:

    [tex] \vec{B} = 30*H*Cos \theta * \hat{x} + 30*H*Sin \theta *\hat{y} [/tex]

    And then you have your Destination vector:

    [tex] \vec{D} = 8000*Cos45*\hat{x} + 8000*Sin45 * \hat{y} [/tex]

    Since you know

    [tex] \vec{D} = \vec{A} + \vec{B} [/tex]

    Then solve for the angle.
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