Swinging on a rope problem

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Homework Statement


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


Homework Equations



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

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?
 
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Answers and Replies

  • #2
TSny
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##L## is not the side adjacent in the right triangle.
 

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  • #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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