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Further investigation of classic ladder problem

  1. Feb 28, 2012 #1
    1. The problem statement, all variables and given/known data

    I already know the answer, and know "how" to get the answer to this problem:


    A 10 foot ft ladder leans against a wall at an angle θ with the horizontal [ground], as shown in the accompanying figure (the figure is of a ladder leaning against a wall). The top of the ladder is x feet above the ground. If the bottom of the ladder is pushed toward the wall, find the rate at which x changes with respect to θ when θ = 60 degrees. Express the answer in units of feet/degree.

    My question is:

    I understand that a rate is a derivative. And derivatives are expressed as tangent lines to a function on a graph. So I am wondering how this ladder problem would be expressed on a graph. Could it be expressed on the cartesian coordinate system? What would it look like? What would the x coordinates and y coordinates be?
     
  2. jcsd
  3. Feb 28, 2012 #2

    Ray Vickson

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    Just figure out what x is as a function of θ.

    RGV
     
  4. Feb 28, 2012 #3
    So for example, if I had a position vs time graph, that means the y axis would be a position axis and the x axis would be a time axis.

    So are you saying that in this case, the y axis should be an "angle" axis and the x axis should be a position axis? So that I have an "angle vs position" graph?
     
  5. Feb 28, 2012 #4

    I still don't know what you mean. This is a function in terms of θ. Sinθ=x/10, so maybe i don't understand the terminology. What do you mean find out what x is as a function of θ? Are you saying find dx/dθ? I already found that to be 5ft/rad. But in terminology, I would have thought it would be said like this: "find derivative of x in terms of θ" ...so is that the same thing as saying: "find x as a function of θ"?
     
  6. Feb 28, 2012 #5
    So you're saying I could represent it on trig graph like this?:

    http://en.wikipedia.org/wiki/File:Sine.svg

    Where the horizontal axis would be the angles and the vertical axis would be the height? So then the derivative of sin(60) would be cos60, or 1/2? So the slope or rate is 5?
     
  7. Feb 28, 2012 #6

    Ray Vickson

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    For every θ between 1 and π/2 you can figure out what x must be to match that θ. So, YES, you get a function x = f(θ), and its derivative df/dθ give you exactly what the question asks for, if you go back and read it again.

    RGV
     
  8. Feb 28, 2012 #7
    Right, but I already got the answer that the question asks for....I know that its 5ft/rad. I'm not confused about how to solve this question for the correct answer.


    My question is, how is that represented on a coordinate system? (that is not part of any assigned question)

    Which coordinate system should I use? (that is not part of any assigned question)

    Where are you getting n/2 from? (that is not part of any assigned question)

    Its just wondering how a scenario of a ladder moving would look if graphed. I can't picture it.

    Am I on the right track with the sin graph?
     
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