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Swinging on a rope problem

  1. Oct 13, 2013 #1
    1. The problem statement, all variables and given/known data
    A hiker plans to swing on a rope across a ravine in the mountains, as illustrated in the figure, where L = 4.0 m and x = 1.8 m, and to drop when she is just above the far edge. At what minimum horizontal speed should she be moving when she starts to swing(in m/s)?

    TNDhEC6.gif

    2. Relevant equations

    Ei= Ef
    So...
    Ke = Pe
    So...
    1/2mv2=mgh

    3. The attempt at a solution

    I have the equation set up correctly but I just don't know how to find h so I can find V

    1/2mv2=mgh

    The Rope makes a isosceles triangle shape so I thought of L as adjacent, and X as the Opposite so I could solve for theta by doing Θ = arctan(1.8/4.0) = 24.22º. However, upon looking at the answer online- it says to take the arcsin(1.8/4.0) = 26.7º. Why is this?
     
    Last edited: Oct 13, 2013
  2. jcsd
  3. Oct 13, 2013 #2

    TSny

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    ##L## is not the side adjacent in the right triangle.
     

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  4. Oct 14, 2013 #3

    Simon Bridge

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    For that matter, x is not the base of an isosceles triangle, as TSny's diagram illustrates.
    That is not the formula for finding the apex angle of an isosceles triangle anyway.
    As TSny says: ##x\neq L\tan\theta## either.

    I'm kinda puzzled that they want you to find the angle at all.
    Since you know L and x, why not find h by pythagoras?
     
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