Treasure Hunt: Adding Vectors for Displacement

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The discussion revolves around calculating the displacement components from a treasure map's instructions. Participants are tasked with finding the northward and eastward displacement magnitudes after following specific directions: walking east, then northwest, and finally north. The importance of showing prior attempts at solving the problem is emphasized to facilitate better guidance. The conversation encourages collaboration and sharing of methods to arrive at the solution. Overall, the focus is on applying vector analysis to determine displacement in specified directions.
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You are on a treasure hunt and your map says "Walk due east for 52 paces, then walk 29.6° north of west for 44 paces, and finally walk due north for 25 paces."
(a) What is the magnitude of the component of your displacement in the direction due north?
b) What is the magnitude of the component of your displacement in the direction due east?
 
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Thread 'Magnitude of buoyant force in fluids of different densities'

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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