How to find displacement in vector diagram?

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To find displacement in a vector diagram, first combine the individual movements in the north-south and east-west directions. Mr. Hinsley's net movements result in 176.5 m north and 256 m east. The total displacement can be calculated by drawing a line from the starting point to the endpoint, forming a right triangle. Apply the Pythagorean theorem to find the hypotenuse, which represents the total displacement. This method effectively summarizes the overall change in position.
karis scherer
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how to find displacement in vector diagram?

My homework question states :
"Mr. Hinsley walks north 252 m, east 512 m, south 35.5 m and finally west 256 m. What is the total distance traveled? What is his displacement?"

I got that the total distance = 1096 m
However i am having trouble finding the displacement. i made a vector diagram but don't quite know how to use it to find the displacement.




! combined north and south. i also combined east and west. i came to the conclusion that he ended up at 176.5 m north and 256 m east. i just don't know what to do from here.

 
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Each leg of the journey is a displacement. Displacement, as you've realized, is a vector.
The sum of all the displacement vectors is the total displacement.
Do you know how to add vectors?
 
Draw a line from the origin to your point. You should now see a right triangle. Use the pythagorean theorem.
 
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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