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How far away will the ball land?

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data
    A ball rolls off an incline at a velocity of 22m/s. The angle of the incline is 32deg, and the height of the incline from the floor is 9m. Assume no air resistance.


    2. Relevant equations
    vf^2=vi^2+2ad
    d=vit+1/2at^2


    3. The attempt at a solution
    I figured i should attempt to separate the motion of the ball into the x and y dimensions first so this was my attempt:
    y motion
    ---------
    22sin32*=11.7m/s
    d=9m
    vf=17.7m/s
    a=-9.8
    t=0.74

    x motion
    ----------
    vi=vf=18.7m/s because 22cos32=18.7m/s
    t=0.74s

    the answer is 11m, but i don't know how to get this answer...please help?
     
  2. jcsd
  3. Nov 28, 2009 #2

    Doc Al

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    Staff: Mentor

    How did you solve for the time?
     
  4. Nov 28, 2009 #3
    time
    -----
    9=11.7t+1/2(-9.8)t^2
    9=11.7t - 4.9t^2
    -2.7/-4.9=.55
    sqrt .55=.74s
     
  5. Nov 28, 2009 #4

    Doc Al

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    Careful: Check the sign of your 'd' and 'vi'.
     
  6. Nov 28, 2009 #5
    oops...I guess 'd' is -9 because it is pointing down? And 'vi' is -11.7 because of direction too?
    I got a new time of .64s
    If the above is correct, i still don't know how to solve this problem...help please? Thank you.
     
  7. Nov 28, 2009 #6

    Doc Al

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    Yes.
    My answer is close to that.
    Now consider the horizontal motion. You have the speed and the time.
     
  8. Nov 28, 2009 #7
    d=vt
    So, d= (18.7)0.64
    = 11.9m
    Is that correct for distance?
     
  9. Nov 28, 2009 #8

    Doc Al

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    That's the correct method. My answer is a bit less; try doing the calculation with more accuracy until the end.
     
  10. Nov 28, 2009 #9
    Yes okay thank you, because it looks like the answer in the book is around 0.9 metres less than my value. How do i calculate with more accuracy throughout in the future please?
     
  11. Nov 28, 2009 #10

    Doc Al

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    Just carry all intermediate values with more digits. Round off only at the end. For example, instead of 22sin32 = 11.7, use 11.66. And so on.
     
  12. Nov 28, 2009 #11
    Thank you for all your help! I can see where my answers have been off marginally on previous problems due to rounding off the intermediate values too soon as it were. :smile:
     
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