Jean's wrath

Wolverine and Jean somehow find themselves in an intense mutant show off in outer space. Assume their positions can be described with coordinate points . Wolverine who was initially standing at the origin (\(0,0,0)\), decides to avoid the conflict and jumps in a straight line towards the point \((3,3,0)\).

Jean, angered by this display of cowardice, uses her telekinetic powers to apply a force of \[ \large{\vec F(x,y,z) = -kxy^2 \hat{\jmath} }\] on Wolverine. This is a force in the negative \(y\) direction whose magnitude depends on Wolverine's position \((x,y,z)\). Calculate the amount of work Jean does on wolverine as he jumps from \((0,0,0)\) towards \((3,3,0)\). If this work is \(W\), input \(|W|\) in joules as your answer.

Take \(k=2.50 \frac{N}{m^3} \)

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