Calculating Force for an Exceptional Standing Jump: Physics Homework Problem

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To calculate the force exerted by a 66 kg person for a standing jump of 0.80 m, the work-energy principle is applied. The gravitational force acting on the person is calculated as 9.81 m/s² multiplied by their mass, resulting in a force of approximately 649.46 N. The total work done to achieve the jump height is calculated as the force times the jump height, yielding 517.968 J. However, the crouching distance of 0.20 m must also be considered, as it affects the force applied during the jump. Overall, the initial calculations provide a foundation, but further refinement is needed to incorporate the crouching distance effectively.
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Homework Statement


An exceptional standing jump would raise a person 0.80m off the ground. To do this, what force must a 66 kg person exert against the ground?
Assume the person crouches a distance of 0.20 m prior to jumping,and thus the upward force has this distance to act over before he leaves the ground.



This question i don't even know how to start
can some one explain how to even start it?
 
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Work = Force * Distance
Force = (9.81)(66)
Work = (9.81)(66)(.80)
Work = 517.968 J

Doesn't account for the crouching distance, but it may be irrelevant, someone else will probably cover that. I hope I went in the right direction with this.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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