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Can anybody display the maths?

  1. Jan 5, 2012 #1
    From another forum

    Can you work this one out?


    It's supposed to be a ladder resting on a barrel. We've guessed the answer will be 12ft, and proven it with CAD! What the maths behind it?
  2. jcsd
  3. Jan 5, 2012 #2
    I'd of thought that there isn't enough information there to give an answer! A height would have to be known? :s
  4. Jan 5, 2012 #3
    A height is known. Look carefully.
  5. Jan 5, 2012 #4


    Staff: Mentor

    there's enough info although it can't be solved simply thru geometry and algebra. You basically have three constraints:
    1) ladder top constrainted to move along y-axis (ie xtop=0 and 0<ytop<12.5)
    2) ladder bottom constrainted to x-axis (ie 0<xbot<12.5 and ybot=0
    3) ladder is tangent to circle

    you can use the pythagorean theorem to relate xbot and ytop to the 12.5

    you need an equation for constraint #3
  6. Jan 5, 2012 #5
    You've obviously got its height of 3 at a depth 1.5 from the y axis. So would you have to use the equation of the circle and then differentiate it?
  7. Jan 5, 2012 #6
    I've considered similar triangles but as previously mentioned there isn't the correct info there I don't think.
  8. Jan 5, 2012 #7
    Sorted it, can be done with Pythagoras!
  9. Jan 5, 2012 #8


    Staff: Mentor

    solved it right?

    "Sorted it" sounds like something from Harry Potter's sorting hat.

    Also could you tell us how you did it.
  10. Jan 6, 2012 #9
    Attached the file of the workings, it almost was magic :p

    Attached Files:

  11. Jan 6, 2012 #10

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Very nice, using the equation for the radius of an inscribed circle. Much simpler than solving for the angle.
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