Resultant displacment and magnitude

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The discussion revolves around calculating the magnitude of a second displacement after a man pushes a mop, resulting in two displacements. The first displacement is 235 cm at an angle of 131° with the positive x-axis, while the resultant displacement is 215 cm at an angle of 49°. The participant is struggling to apply the formula R=√(A²+B²-2AB(cos(Φ)) and seeks clarification on their approach. They are advised to find the x and y components of both displacements and use vector subtraction to determine the second displacement. The conversation emphasizes the importance of correctly breaking down the vector components for accurate calculations.
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Homework Statement


A man pushes a mop across the floor causes the mop to undergo two displacements. The first has a magnitude of 235cm and makes an angle of 131⁰ with the positive x-axis.

The resultant displacement has a magnitude of 215cm and is directed at an angle of 49⁰ to the positive x-axis.

Find the magnitude of the second displacement. Answer in units of cm.

Homework Equations



R=√(Aˆ2+Bˆ2-2AB(cos(Φ)))

Sinβ=B/R(Sin(Φ))

The Attempt at a Solution



Tried using the above equation and not getting the right answer.
What am i doing wrong?
I set
R=215
A=235
B=X second displacement
Φ=49⁰
 
Physics news on Phys.org
A+B=R implies B=R-A. Find the x and y components of R and A, then recall how to subtract two vectors when you know their components.
 
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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