Solve Free Falling Object: Find Height of Ball

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A ball dropped from rest covers three-fifths of the distance to the ground in the last second of its fall, prompting a calculation of the initial height. The user initially struggled with kinematic equations to derive the height but was unable to find the correct answer after extensive effort. Eventually, the user resolved the problem independently without needing further assistance. The discussion highlights the challenges of applying kinematic equations in free-fall scenarios. Ultimately, the user successfully determined the height from which the ball was dropped.
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Homework Statement


A ball, dropped from rest, covers three-fifths of the distance to the ground in the last second of its fall. From what height was the ball dropped?

The Attempt at a Solution


I have spent the past thirty minutes attempting to figure this out. I initially used a kinematic equation which gave me a new expression for the height and I attempted to put that expression into another kinematic equation but I still cannot seem to arrive at the correct answer.

Any advice or help on this would be appreciated!
 
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No need, I finally figured it out :)
 
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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