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Homework Help: A ball rolls off a table

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data
    A ball rolls off a table with a horizontal v of 8m/s. If it takes the ball .22s to hit the floor, how high was the shelf?


    2. Relevant equations
    d=Vot+1/2at²


    3. The attempt at a solution
    HORIZ
    a=0
    Vo=8m/s
    V=8m/s
    d=?
    t=.22s

    d= (8)(.22)+1/2(8)(.22²)

    Is the hieght of the shelf d=1.997m???
     
  2. jcsd
  3. Jun 8, 2010 #2
    You have to do it all in the Y-direction.

    Vo = 0
    t = 0.22
    a = gravity

    d=Vot+1/2at²

    solve for d
     
  4. Jun 8, 2010 #3
    correction d= (8)(.22)+1/2(0)(.22²)
    d= (8)(.22)
    d= 1.76
     
  5. Jun 8, 2010 #4
    ok Vertical
    a= -9.8m/s
    Vo=0
    V=?
    d=9.8m
    t=.22

    (9.8)(.22)+1/2(9.8)(.22²)
    d= 2.39
     
  6. Jun 8, 2010 #5
    Recheck your working, you made a mistake

    Your equation there is:

    at+1/2at2 instead of Vot+1/2at2

    its just 1/2(9.8)(.222)
     
  7. Jun 8, 2010 #6
    ok vert= .24 and horz=1.76

    what do I do with these 2 distances
     
  8. Jun 8, 2010 #7
    The vertical distance is the height of the shelf
     
  9. Jun 8, 2010 #8
    so, I only needed to find the vertical distance? I did the horz distance for no reason...

    and why do i only need half of the equation?
     
  10. Jun 8, 2010 #9
    You didn't really only need half, but since Vo = 0, then Vot = 0

    so Vot+1/2at2 = 0 + 1/2at2
     
  11. Jun 8, 2010 #10
    ok...
    The next problem is this

    A ball rolls off a table which is 2.8m high. If it leaves the table with a horizontal v of 8m/s, calc the distance from the base of the shelf at which the ball will strike the ground.

    I know i need to figure out how long it will take the ball to strike the ground. then use that to find the horz distance

    vert d= 1.41

    8(1.41)= 11.28m
     
  12. Jun 8, 2010 #11
    You're theory is right, but your answer confuses me, what is that?

    How are you finding the time the ball takes to hit the ground?
     
  13. Jun 8, 2010 #12
    i tried to quickly do all the work haha

    vert distance
    a= -9.8m/s
    Vo=0
    V=?
    d=9.8m
    t=?

    using at+1/2at²

    9.8= 1/2(9.8)t²

    2(9.8)=9.8t²
    over
    9.8=9.8
    (the 9.8's cancel leaving)

    2=t²

    t=square root of 2

    t= 1.41


    soo it will take 1.41s for the ball to hit the ground.

    using t= 1.41 i can now find the horz distace

    a=0
    Vo=8
    V=8
    d=?
    t=1.41

    d= Vot

    8(1.41)= 11.28m
     
  14. Jun 8, 2010 #13
    Well, your method of working is correct, but in the very beginning you used the wrong value of d

    "A ball rolls off a table which is 2.8m high" not 9.8 like you used
     
  15. Jun 8, 2010 #14
    ok

    2.8m= 1/2(9.8)t²

    2(2.8)=2(1/2)(9.8)t²

    5.6m= 9.8t²
    Divide 9.8 to both sides

    .5714=t²

    t=.756s

    d=Vot
    d=8(.756)
    d=6.048
     
  16. Jun 9, 2010 #15
    Does the final anwser look correct?
     
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