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Homework Help: Particle on a position vector.

  1. Feb 25, 2015 #1

    Yam

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    1. The problem statement, all variables and given/known data
    A particle moves in a plane described by the position vector r (t)= ( 2bsin( wt ))i + ( bcos( wt ) )j
    where b and w are some constants. The angle between its velocity and acceleration vectors at time t=(π/2w)

    a) is approximately 27 degree .
    b) is exactly 45 degree .
    c) is approximately 63 degree .
    d) is exactly 90 degree .
    e) cannot be determined since b and w are not specified.

    2. Relevant equations
    differentiation

    3. The attempt at a solution
    v(t) = (2bw(cos(wt)))i + (-bw(sin(wt))j
    a(t) = (-2bww(sin(wt)))i + (-bww(cos(wt)))j

    After that, how do i find the angles?
     

    Attached Files:

  2. jcsd
  3. Feb 25, 2015 #2

    SteamKing

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    How would you normally find the angle between two vectors?
     
  4. Feb 25, 2015 #3

    haruspex

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    What do you know about the dot product of two vectors?
     
  5. Feb 25, 2015 #4

    Yam

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    I see, the dot product would represent the angle between 2 vectors. Gimme some time to work the exact solution out
     
  6. Feb 26, 2015 #5

    Yam

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    Hi, is this formula correct? Or is this only for coordinates only?

    So, the solution is Cos-1(0)=90 degrees?
     

    Attached Files:

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    Last edited: Feb 26, 2015
  7. Feb 26, 2015 #6

    haruspex

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    That's the right formula, but how do you get 0 for the dot product?
     
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