Question

Batman, whose mass is 122 kg, is holding on to the free end of a 6.89 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 77.8 ◦ 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 this maneuver? Answer in units of J.

Answer 1

6496.854532 J

Step-by-step explanation:

m = Mass of batman = 122 kg

g = Acceleration due to gravity = 9.8 m/s²

The distance to the ground is given by

`h=6.89-6.89cos77.8\\\Rightarrow h=5.43397\ m`

The work done will be the potential energy

`W=mgh\\\Rightarrow W=122* 9.8* 5.43397\\\Rightarrow W=6496.854532\ J`

The work done against the force of gravity in this maneuver is 6496.854532 J