Inelastic Collision Derivation Help

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The discussion focuses on deriving the equation for inelastic collisions, specifically addressing the conservation of momentum and the coefficient of restitution. The second equation presented needs correction to accurately reflect the relationship between final velocities. To derive the desired equation, one should multiply the corrected second equation by the mass of the second object and combine it with the momentum equation. The importance of solving the linear system of equations is emphasized, as well as the necessity of actively engaging in the derivation process. Understanding these principles is crucial for mastering inelastic collision calculations.
GreenSabbath
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http://upload.wikimedia.org/math/5/c/b/5cbdceba601a68315f744dc1c06e9ba7.png"
How wxactly has this equation be derived?

http://upload.wikimedia.org/math/3/c/5/3c53f3d1c66725053decc7e3e546c32d.png"
Can someone help me with the derivation. I can't trace the orgin of the second part od the systems of equation.

Help needed urgently Thanks
 
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Not clear what your question is. Those two equations in your second link:
(1) Looks like conservation of momentum (OK)
(2) Looks like "c" is the coefficient of restitution (not quite right)

You'll have to fix the second equation. It should read:
V_{1f} - V_{2f} = c(V_2 - V_1)

Then, to combine those equations to get the equation in your first link: multiply the 2nd equation by M2 and add it to the first equation. Isolate V1f.
 
You derive it by perseverance.
Solve the linear system of equations you are supposed to solve.

If you don't have the skill to solve a system of linear equations, that is what you should focus on.

If you can't be bothered to perform the operations yourself, there is no reason for us to help you out, is there?
 
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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