Bird on a bus -- friction problem

quark12
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Homework Statement
i attached the problem and my solution, is my solution right? thank you
Relevant Equations
f=ma
1606159179290.png
 

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In your second part ##V_0 = 0## other than that everything looks good to me.
 
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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