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Staircase projectile

  1. Jul 26, 2006 #1
    A ball rolls out from the top of the stair case, with a horizontal velocity of 5 ft/s. Each step is 8 inches wide and 8 inches long. Which step will the ball hit first?

    My problem:
    I'm stuck on how to handle the problem. Where do you start thinking?
  2. jcsd
  3. Jul 26, 2006 #2
    You could try trial and error.
    First, see if the ball will hit the first step.
    If not, then see if the ball will hit the second step.
    If not, then see if the ball will hit the third step.

    Useful formulas:

    [tex]t_{falling} = \sqrt{\frac{2h}{g}[/tex]

    [tex]x_{max} = v_0\sqrt{\frac{2h}{g}[/tex]

    Maybe there is a better method to solve the exercise. But that's the only one I see. Hope it helps! :wink:
    Last edited by a moderator: Jul 26, 2006
  4. Jul 26, 2006 #3


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    See when the ball drops below the line joining the edges of the steps. It will hit the step that is immediately below the point where it crosses that line.
  5. Jul 26, 2006 #4


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    Keep in mind the ball falls in a parabolic motion
  6. Jul 26, 2006 #5


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    Last edited: Jul 26, 2006
  7. Jul 28, 2006 #6
    wow... thanks! how'd you think of that?
  8. Aug 1, 2006 #7
    let it fall on the nth step
    v along x=5cos theta
    n*8(length of the step)=vcostheta*t
    here theta=0(thrown along the x axis)
    similarly proceed in y direction and finally equate t in both the eqn
    Last edited: Aug 1, 2006
  9. Aug 3, 2006 #8
    thank you very much!
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