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Vector Components Question

  1. Sep 28, 2011 #1
    What are the resultant components of the vectors?

    1. The problem statement, all variables and given/known data

    Determine the sum of the following three vectors. Give the resultant in terms of a. components, b. magnitude and angle with x-axis.

    Vector A has a magnitude of 66 at an angle of 28 degrees northeast (quadrant 1)
    Vector B has a magnitude of 40 at an angle of 56 degrees northwest (quadrant 2)
    Vector C has a magnitude of 46.8 at an angle of 0 (on y-axis between Quadrant 3 and 4)

    2. Relevant equations

    Vx = Dcos0
    Vy = Dsin0
    Vx = V1x+V2x+V3x
    Vy = V1y+V2y+V3y
    Vy/Vx = tan θ


    3. The attempt at a solution

    So here is how I started

    A: Vx = +(66)(cos 28) = 58.27454
    Vy = +(66) (sin 28) = 30.985

    B: Vx = -(40)(cos 56) = -22.3677
    Vy = +(40)(sin 56) = 33.1615

    C: Vx = (46.8)(cos 0) = 46.8
    Vy = (46.8) (sin 0) = 0

    Then I would add the three parts of Vx to get overall Vx (58.27454-22.3677+46.8) = 82.70684 & the three parts of Vy to get overall Vy (30.085+33.1615+0) = 63.2467.

    This means the components would be (82.70684, 63.2467) and I would continue with pythagorean theorem to get the magnitude & use the arctan formula to get the angle. However, my answer for components is incorrect, the book says it should be (35.9,17.3). What did I do wrong? Thank you so much in advance.
     
    Last edited: Sep 28, 2011
  2. jcsd
  3. Sep 28, 2011 #2
    Your computation for vector C is wrong. I get their answer. How can it have an x component when it lies on the y axis?
     
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