1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook