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Batman, whose mass is 89.5 kg, is holding on to the free end of a 13.4 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 72.4 ◦ 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 :

Answer:

[tex] 8.2\times 10^{3}[/tex] J

Explanation:

[tex]L[/tex] = length of the rope connected = 13.4 m

[tex]\theta[/tex] = Angle made by the rope with the vertical = 72.4°

[tex]h[/tex] = height gained by the batman above the reference point  

Height gained by the batman above the reference point  is given as

[tex]h = L(1 - Cos\theta )[/tex]

[tex]m[/tex] = mass of batman = 89.5 kg

[tex]g[/tex] = acceleration due to gravity = 9.8 ms⁻²

Work done against gravity is same as the gravitational potential energy gained by batman and is given as

[tex]W = mgh[/tex]

[tex]W = mgL(1 - Cos\theta )[/tex]

Inserting the above values

[tex]W = (89.5)(9.8)(13.4)(1 - Cos72.4 )[/tex]

[tex]W = 8.2\times 10^{3}[/tex] J

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