Vectors physics homework -- Addition of two vector forces

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The discussion focuses on a user's difficulty in solving a physics homework problem involving vector forces. The attachment provided is difficult to read, prompting requests for the user to type out their work directly in the forum for clarity. Participants point out that there is confusion due to incorrect labeling of variables, which complicates understanding. Suggestions include using math symbols available in the forum's edit bar and finding relevant equations to aid in the solution. Clear communication and proper formatting are emphasized to facilitate assistance.
Ahmad Qaimari
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Homework Statement
Two forces.. F and 2F..the angle between them is x prove that their resultant is R=root square(1+8cos^2 x/2) X F
Relevant Equations
R=root square(1+8cos^2 x/2) X F
Trying to solve it
 

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Welcome to the PF.

Your attachment is sideways and pretty hard to read. Can you please type your work into the forum? That makes it a lot easier to respond.

There are math symbols in the Edit bar above the edit window under the √ symbol, and there is a tutorial about how to use LaTeX under the Help pages (see INFO at the top of the page). Thanks. :smile:
 
Hello Ahmad, :welcome: !

My neck still hurts from trying to read your picture ( I use a desktop, not a phone). For the sake of others I re-post it:
1567439733353.png

I notice your x is not the ##x## in the exercise (which is your ##\theta### ) so that deciphering isn't just painful, but also confusing.
As @berkeman (who types faster:frown:) says: could you re-post and explain what it is you write down?

In the mean time you can try to find a relevant equation that links ##\cos\theta## and ##\cos(\theta/2)## and post that too :smile:

Oh, and: read this
 
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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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