Batman, who\'s mass is 80.0 kg holds onto the free end of a 12.0 m rope, the oth

Question

Batman, who's mass is 80.0 kg holds onto the free end of a 12.0 m rope, the other end of which is attached to a tree limb above. He puts the rope into motion as only Batman knows hpw, eventually getting it to swing enough that he can reach a ledge when the rope makes an angle of 60 degrees with the downward vertical. How much work is done against the force of gravity?

The answer is given, but i'm not able to get it. the answer is 4,700 J. I just need talked through how to actually go about doing the problem.

Explanation / Answer

Ok so we are trying to find work against gravity.
Work is represented by the formula
W=Fd,
We need to find the change in vertical height of batman once he swings that 60 degrees.
It would be best for you to draw a triangle. Draw a straight line down first for the length of the rope, and then swing it over about 60 degrees. You should notice that the end of the rope be higher. Noe connect the new height of the rope with a horizontal line to the original rope. You can see that the unknown angle is 30 degrees(its a right triangle) so taking the sin of 30 we get the vertical height of the triangle over the hypotenuse the length of the rope.
solve for the height
sin = y/hyp

y=sin*hyp

y=12sin30o = 6m

Now subtract this hieght from the vertical hieght and you will get the vertical displacement. (6m)

Now plug this into the original work equation.

W=Fd

W=mgd

W=(80.0kg)(9.8m/s2)(6) = 4704J

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