Factors that determine direction an object will move after an elastic collision?

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The direction an object will move after an elastic collision is primarily determined by the initial velocities and masses of the colliding objects. Knowing these factors allows for the calculation of post-collision velocities, which are vector quantities that include direction. The conservation of momentum and kinetic energy principles also play crucial roles in predicting the outcome of the collision. Accurate measurements of these variables are essential for precise predictions. Understanding these dynamics is fundamental in physics and engineering applications.
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Initial velocities and masses of the objects colliding...?
 
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Yes, if they are known then the velocities after collision (which are vectors so include direction) can be determined.
 
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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