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Displacement vectors

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data

    Three displacement vectors of a croquet ball are shown in the figure, where |a vector| = 22.0 units, |b vector| = 25.0 units, and |c vector| = 10.0 units.

    (a) find the resultant in unit-vector notation

    ____ i hat + ____ j hat

    (b) Find the magnitude and direction of the resultant displacement.
    ____ units
    ____ ° (from the +x axis)

    2. Relevant equations

    [​IMG][​IMG]



    3. The attempt at a solution

    I'm completely stumped. Can someone please teach me how to start this problem? Thank you.
     

    Attached Files:

  2. jcsd
  3. Sep 28, 2008 #2

    Integral

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    Staff Emeritus
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    Gold Member

    This is very similar to the last problem I helped you with. Decompose each vector to x and y components. Add 'em all up.
    A unit vector has magnitude 1 so you will need to "normalize" your result. That is divide each component by the magnitude of the resultant vector.
     
  4. Sep 28, 2008 #3
    how do I get the resultant in unit-vector notation?
     
  5. Sep 29, 2008 #4
    can someone please check if my work and answer is correct?

    |a vector| = 22* cos 90 = 0 ; 22* sin 90 = 22
    |b vector| = 25*cos 45 = 17.68 ; 25*sin 45 = 17.68
    |c vector| = 10*cos -45 = 7.07 ; 10*sin -45 = -7.07

    Fx = 24.75 Fy = 32.61

    24.75^2 + 32.61^2 = c^2
    c = 40.94

    tan^-1 (32.61/24.75) = 52.80 degrees

    (a) 24.75 i hat + 46.75 j hat
    (b) 52.9 units; 62.10 degrees
     
    Last edited: Sep 29, 2008
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