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Kinematics problem-finding acceleration

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Hi everyone! This is my homework question, an easy one, but I cannot find my mistake. Any help will be greatly appreciated.

    Mary and Sally are in a foot race. When Mary is 22 m/s from the finish line, she has a speed of 4.0 m/s and is 5.0 m behind Sally, who has a speed of 5.0 m/s. During the remaining portion of the race, Sally decelerates at a constant rate of 0.48 m/s2 to the finish line.

    What constant acceleration does Mary now need during the remaining portion of the race, if she wishes to cross the finish line side-by-side with Sally?

    2. Relevant equations



    3. The attempt at a solution
    (The final velocity of Sally)=Vsf2
    (The initial velocity of Sally)=Vsi2
    Vsf2:Vsi2-2ax
    Vsf2=52-2*0.48*17
    which is 3 m/s.
    Vsf=Vsi+at
    3=5-0.48t
    t=4.16s

    They should finish the race at the same time, so this is also the time in which Mary ran 17 m.

    X=Vot+1/2at2
    22=4*4.16+a*(4.16)2
    5=2.08*4.16*a
    and a=0.60 m/s2

    This is an internet assignment and the program says this result is false.
    Is there a mistake here? What do I do wrong? Thanks for any help :)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 9, 2011 #2

    PeterO

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    Homework Helper

    Your final velocity of 3 m/s is 2.946.... rounded off.
    Not sure you can round off like that during the calculations.

    EDIT: and also Mary had to run 22m. ( she was 5m behind)
     
  4. Oct 9, 2011 #3

    Doc Al

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    Staff: Mentor

    Be careful about rounding off your intermediate calculations. For example, don't round off Sally's final speed to 3 m/s--that introduces errors in all subsequent calculations.
     
  5. Oct 9, 2011 #4
    I did not round off the velocity of Sally, and this time I have t=4.375 s. When I do calculations according to the new value of t, I find the acceleration of Mary as 0.47 m/s^2. I still cannot figure out my mistake, and I used my last chance to answer it. Anyways, this question is a pain in the neck for me for a week.

    My mistake that Mary ran 17 m, but I didn't do my calculations according to this mistake.
    Thanks for your help :)
     
  6. Oct 9, 2011 #5

    Doc Al

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    Staff: Mentor

    I got 4.279 s.
     
  7. Oct 9, 2011 #6
    That's true! I have no idea how I could find 4.375 s.

    Then

    22=4t+1/2at2
    22-17.116=9.154a
    4.884=9.154a
    a=0.53m/s2

    I should have been more careful with my calculations and rounding off... I've lost 20 points already, but at least I could solve it. Thanks a lot for your help, Doc Al :)
     
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