Problem with geometry in conservation of energy problem

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insomniac1
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My problem is with where the initial height being R - R cos theta. I don't really get where that came from. any hints on where i could look to find the answer or suggestions on how to start are greatly appreciated.

nevermind i figured it out
 
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  • Diagram of a stage apparatus: an actor in a harness hangs from a steel cable running over pulleys to a sandbag on the floor, with the cable length R and angle theta from the vertical marked, and the actor's initial height y_i labeled.
    Selection_001.png
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  • Text reading: From the geometry in Figure 8.5a, notice that y_f = 0, so y_i = R - R cos θ = R(1 - cos θ). Use this relationship in Equation (1) and solve for v_f^2. Equation shown: v_f^2 = 2gR(1 - cos θ).
    Selection_002.png
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Last edited:
Hello insomniac1. Welcome to PF!

In the figure shown in the problem statement, construct a right triangle where the hypotenuse is the cable of length R as drawn in the figure, another side of the triangle runs vertically from the pulley (extend the dotted line shown), and the third side is horizontal from the man to the vertical side of the triangle. Can you use that triangle to help you see where the expression R - Rcosθ comes from?

(If you want to access symbols like θ, click on the "Go Advanced" button below the reply box.)