Solve 3D Kinematics Problem with Homework Equations | Attempted Solution

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The discussion focuses on solving a 3D kinematics problem related to the horizontal range of a plane. The original poster expresses confusion over their interpretation of the horizontal range, believing it to be a distance to the east rather than a distance from the radar site excluding altitude. A participant clarifies that the horizontal range refers to the plane's distance without considering its altitude, emphasizing the correct interpretation of horizontal in terms of x and y coordinates. The original poster acknowledges this misunderstanding and appreciates the clarification. This exchange highlights the importance of accurately interpreting terminology in physics problems.
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Homework Statement


I know pictures aren't the best, but here it is.
7gkPxQB.png



Homework Equations





The Attempt at a Solution


This is my work for this problem. Disregard the drawing as it isn't right.

I'm not sure if I'm misinterpreting the horizontal range part or what. I feel pretty confident about my work but webassign says it's wrong and I don't really see why.
phYjMsvl.jpg

Link to original if it's not big enough
 
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The horizontal range of the plane means its distance from the radar site without including the plane's altitude.
You are treating the horizontal range as the distance to the east, which is incorrect.
 
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SteamKing said:
The horizontal range of the plane means its distance from the radar site without including the plane's altitude.
You are treating the horizontal range as the distance to the east, which is incorrect.

Ahhh. You were absolutely spot on. I was unaware that they were using horizontal in the sense of x and y. Thank you very much.
 
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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