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Calculating Displacement with Vectors!

  1. Sep 17, 2011 #1
    1. The problem statement, all variables and given/known data
    Hello, I have a homework question that I'm having difficulty with, it is:
    A car travels due east (bearing 90) from point A for 6km to point B and then North-west (bearing 315) for 4.0km to point C.
    By constructing a vector diagram, or otherwise, find the resultant displacement (magnitude and direction) of the car at point C from A.


    2. Relevant equations
    I don't think pythagoras theorem works here, as there is no right-angled triangle present. Although, I may be incorrect.



    3. The attempt at a solution
    I've drawn a vector diagram, head to tail, and measured the displacement, it comes to 4.3km at a bearing of 50. Is that correct?
     
  2. jcsd
  3. Sep 17, 2011 #2
    You can try other methods of finding vector C, you can find the components of vector A, and vector b

    Remember finding the magnitude or resultant vector is
    [itex]\vec{R}[/itex] = [itex]\vec{A}[/itex] + [itex]\vec{B}[/itex]

    which is really
    [itex]\vec{R}[/itex] = (A[itex]_{x}[/itex] ) (B[itex]_{x}[/itex] ) + (A[itex]_{y}[/itex] ) (B[itex]_{y}[/itex] )

    A[itex]_{y}[/itex] = ([itex]\vec{A}[/itex]) (sin [itex]\theta[/itex])
    A[itex]_{x}[/itex] = ([itex]\vec{A}[/itex]) (cos [itex]\theta[/itex])


    B[itex]_{y}[/itex] = ([itex]\vec{A}[/itex]) (sin [itex]\theta[/itex])
    B[itex]_{x}[/itex] = ([itex]\vec{A}[/itex]) (cos [itex]\theta[/itex])

    The Ax, Ay, Bx, By equations are derived from this idea xycomponents.gif
     
  4. Sep 17, 2011 #3
    I would plug and chug for you, but I'm kind of confused by the bearings.
     
  5. Sep 17, 2011 #4
    Don't rely on measuring the displacement vector. Sometimes the ruler isn't as precise, also it will help you in the long run to have these equations in your tool box.
     
  6. Sep 17, 2011 #5
    Let me know if you solved it, or if it helped. So I can get some personal feedback, cuz I don't want to be misinforming people lol.
     
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