How Much Work Does Batman Do Swinging to a Ledge?

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To calculate the work done by Batman while swinging to a ledge, the formula W = Frcos(theta) is used, where F is the gravitational force and theta is the angle with the vertical. The initial calculation of 2641.08 J is deemed incorrect, prompting questions about the angle used in the calculation. Participants discuss the need to determine the correct angle for the swing and the energy dynamics involved in Batman's maneuver. Clarification is sought on how to calculate the energy difference between the starting and ending positions. Understanding the energy transfer and the correct angle is essential for solving the problem accurately.
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Homework Statement



Batman, whose mass is 101kg, is holding on to the free end of a 16 m rope, the other end of which is fixed to a tree limb above. He is able to get the rope in motion as only Batman knows how, eventually getting it to swing enough that he can reach a ledge when the rope makes a 80.4 degree angle with the vertical. The acceleration for gravity is 9.8m/s^2. How much work is done against the force of gravity in this maneuver? Answer in units of J.

Homework Equations



W= Frcos(theta)

The Attempt at a Solution



W= Frcos(theta)
= (101*9.8)(16)(cos80.4)
= 2641.08 J
= wrong answer

What am I doing wrong? From the looks of it, maybe the angle? If so what angle do I use and how do I find it?
 
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How much more energy does Batman have at the end of the process, compared to at the beginning? Where would that energy come from?
 

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