AP Physics B Course Description Multiple Choice #3-4

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The discussion focuses on solving a physics problem involving forces on an inclined plane, specifically a 30-60-90 triangle. The weight of the object is identified as a downward force, with the normal force acting perpendicular to the plane. The challenge lies in determining the correct equations to use for calculating the components of the weight. The perpendicular component corresponds to the normal force, while the parallel component is responsible for the object's tendency to slide down the plane. Understanding these components is essential for solving the problem effectively.
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Homework Statement


http://apcentral.collegeboard.com/apc/public/repository/ap-physics-course-description.pdf

Page 45

Homework Equations


sinθ = opp/hyp

tanθ = opp/adj

cosθ = adj/hyp

G ≈ 10 m/{s}^2


The Attempt at a Solution


I know that the weight is a force pointing downwards (towards the center of the Earth) and the normal force is perpendicular to the plane. The inclined plane is a 30-60-90 triangle. However, I'm having trouble figuring out which equations to use exactly (our teacher gave these problems to us at the start of AP Physics without any instruction. They are kind of like a heads-up for us to know what kind of questions we should be expecting).
 
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When you split the weight into two components, one perpendicular to the plane and one parallel, the one perpendicular is your normal force and the one parallel is what causes the block to slide down the plane.

So you need to find that parallel component.
 
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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