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Homework Help: Magnitude and direction of resultant

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data

    A car travels 20 km due north and then 35 km in a direction 60 degree west of north. Find the magnitude and direction of the car's resultant displacement.

    2. Relevant equations

    R = sqrt(A^2 + B^2)
    Ax = cosA, Ay = sinA
    tan = y/x

    3. The attempt at a solution

    This question was introduced and solved in the textbook before the author introduced Components of a Vector and Unit Vectors (i, j, z; Ax, Ay, Az).

    I came back to this question as an attempt. The author used law of cosines in his deomonstration, as well as sin beta to solve the angle (direction).
    He gave R = 48.2km at 38.9

    I tried this problem with component method.
    I drew a picture and I started the problem by listing components:

    let the north 20km = A, 35km = B and their resultant = R

    Ax = 0 (by all means, cos90 * 20 gives zero anyway)
    Ay = sin90 * 20 = 20
    Bx = cos60 * 35 = 17.5
    By = sin60 * 35 = 30.3

    ** --> = vector
    --> R = (Ax + Bx)i + (Ay + By)j
    --> R x = Ax + Bx (17.5)
    --> Ry = Ay + By (50.3) and
    --> R = sqrt (Rx^2 + Ry^2)

    In the end, R I got ~ 53 km, and for the degree, I got tan (Ry/Rx) = 70.7, but since the picture shows the direction is beyond 90, I say 180 - 70.7 = 109.3

    Where did I do wrong?

    Thanks.
     
  2. jcsd
  3. Jan 28, 2010 #2

    hage567

    User Avatar
    Homework Helper

    I think your components for your B vector are wrong. Your Bx component should be 35sin60, not 35cos60. Likewise, your By component should be 35cos60 instead of 35sin60. Draw it out carefully and re-check your trig.
     
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