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Vector calculus

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Use the given information to find the position and velocity
    vectors of the particle.

    a(t) = −cos t i − sin t j; v(0) = i; r(0) = j

    2. Relevant equations



    3. The attempt at a solution
    Ok first step integrate a(t).

    which i get to be
    -sin(t)i +cos(t)j + c

    now using the initial condition v(0) = i
    i get v(t) = 1-sin(t)i +cos(t)j

    now integrate v(t)

    = (cos(t)+t)i +sin(t)j
    using initial condition r(0) = j
    r(t) = (cos(t) + t)i + (sin(t)+1)j

    they are my two answers in bold but the back of my book has different answers and i don't know whats going wrong.

    Thanks for the assistance
     
  2. jcsd
  3. Feb 12, 2012 #2

    SammyS

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    Your v(t) is incorrect. It gives you that v(0) = 1 + j. That's neither a vector nor a scalar. You can't add a vector & a scalar.

    The constant, c, you have after integrating a(t) is a vector constant, c.
     
  4. Feb 12, 2012 #3
    so the vector constant should be equal to i no?
     
  5. Feb 12, 2012 #4

    SammyS

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    No, although I see that you may have meant to have v(t) = (1-sin(t))i + cos(t)j. But that still ignores the fact that cos(0) = 1, not zero.
     
  6. Feb 12, 2012 #5
    so the answer must be
    (1-sin(t))i+(cos(t)+1)j ?

    in the book however the answer is given
    (1-sin(t))i+(cos(t)-1)j

    I don't know where I'm going wrong.
    Thanks again.
     
  7. Feb 12, 2012 #6

    SammyS

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    cos(0) - 1 = 1 - 1 =0
     
  8. Feb 12, 2012 #7
    Sorry Sammy I'm still lost :(
     
  9. Feb 12, 2012 #8

    vela

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    How did you come up with your answer? What do you get when you set t=0 in your answer?
     
  10. Feb 12, 2012 #9
    v(0) = -sin(0)i +cos(0)t + c
    = 0i+1j+c
     
  11. Feb 12, 2012 #10

    vela

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    I don't see how you solved for c.
     
  12. Feb 12, 2012 #11
    That's the part I'm stuck at do i set the lhs equal to zero?
     
  13. Feb 12, 2012 #12

    vela

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    What do the initial conditions given in the problem statement say?
     
  14. Feb 12, 2012 #13
    oh I see, thanks.
     
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