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Homework Help: Bee and a spiral

  1. Jan 20, 2009 #1
    1.)

    A bee goes from its hive in a spiral path given in plane polar coordinates by
    r = b*ekt , θ = ct,
    where b, k, c are positive constants. Show that the angle between the velocity vector and the
    acceleration vector remains constant as the bee moves outward. (Hint: Find v · a/va.)

    so here is my v and a

    2.)
    v = (r')er+(r*θ')eθ

    a = (r''+rθ')er+(rθ''+2r'θ')eθ

    r' = bk*ekt
    r'' = bk2ekt
    θ' = c

    3.) my attempt at a solution

    bkekt(bk2ekt-bektc2)+(bektc)(2bkektc)

    is that the right dot product

    this is where i'm stuck
     
  2. jcsd
  3. Jan 20, 2009 #2
    so I got down to this:

    e2kt(a bunch of constants)+e2kt(a bunch of constants)/e4kt


    all the e's cancelled out and left just constants
     
  4. Dec 7, 2011 #3
    My answer is for the dot product is:

    e2kt(b2k3 + b2kc + 2b2kc2)
     
  5. Dec 7, 2011 #4
    you continue by finding the modulus of v and a then by using the hint you cross out the

    b2e2kt and end up with cos-1(a bunch of constants) and the answer
     
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