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A Woman Running Towards a Bus Which Pulls away

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data
    A woman is running at a constant velocity of 5.0m/s in an attempt to catch a bus. When she is 11m from the bus, it pulls away with a constant acceleration of +1.0m/s2. From this point, how much time does it take her to reach the bus if she keeps running with the same velocity?



    2. The attempt at a solution
    Finding the time
    d = di + vit+1/2at2
    0 = 11 + 0t + 1/2(1)t2
    0 = 11 + .5t2
    t = sqrt of 11.5
    t = 3.39

    Distance traveled by woman
    d = v*t
    d = 5*3.39
    d = 16.95m

    Distance traveled by bus
    vf = vi + at
    = 0+1*3.39
    vf = 3.39

    d = 1/2 (vi + vf)t
    d = 1/2 (3.39) 3.39
    d = 1/2 * 11.5
    d = 5.75
    The bus traveled 5.75m, add in the initial distance of 11m
    16.75m

    That's the closest I can get to the answer. Any guidance on where I want wrong? Thanks!
     
  2. jcsd
  3. Oct 9, 2012 #2
    Set your initial position to Zero for woman, and initial position to 11 for the bus. Set these two equations equal to solve.

    Woman d1=0+5t
    Bus d2=11+.5t2

    When both positions are equal she will reach the bus
    d1=d2

    5t = 11+.5t2
    10t-t2 = 22
    t=5±√3

    ______________________________
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    Last edited: Oct 10, 2012
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