Work done against gravity (Batman on a rope)

[staceyrho]

4) Batman, whose mass is 66.7 kg, is holding on to the free end of a 6.52 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 41.4 degrees angle with the vertical. The acceleration of gravity is 9.8 m/s^2. How much work was done against the force of gravity in the maneuver? Answer in units of J.

 

[galactus]

I need to brush up on physics, but Skeeter will correct me if I erred.


\(\displaystyle \L\\W=mg{\Delta}y\)

\(\displaystyle \L\\{\Delta}y={-}cos({\theta})\)


\(\displaystyle \L\\(66.7)(9.8)(6.52)(1-cos(41.4))=1065 \;\ J\)