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Sailboat Race Vectors Paroblem

  1. Sep 12, 2012 #1
    A sailboat race course consists of four legs defined by the displacement vectors A, B, C and Dshown above.
    The values of the angles are Θ1 = 35.00, Θ2 = 34.00, andΘ3 = 20.00.
    The magnitudes of the first three vectors are A = 3.0 km, B = 5.0 km and C = 4.5 km. The finish line of the course coincides with the starting line.
    The coordinate system for this problem has positive x to the right, positive y as up and counter-clockwise to be a positive angle.
    1) What is the distance of the fourth leg?
    2) What is the value of Θ4?
    3) What is the value of Dy?

    To solve the problem I did the following:

    Ax = 3cos35°
    Ay = 3sin35°
    Bx = 5cos146°
    By = 5sin146°
    Cx = 4.5cos 20°
    Cy = 4.5sin20°

    Somehow I was able to get the right answer of the fourth leg but not for Dy or the angle.
     

    Attached Files:

  2. jcsd
  3. Sep 12, 2012 #2

    rl.bhat

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    Homework Helper

    From the given data, you can find the angle between A and B. From that you can find the resultant R of A and B using cosine rule. Next using sine rule, you can find the angle between A and R and B and R. That gives you the angle between R and C. Similarly proceed to find the fourth leg and θ4.
     
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