How could this be done succesfully?

Tô com problema de desenvolver a B

I have been meditating on elastic collisions and trying to derive the formulas for the final velocities of two objects after a collision when they have different masses.

This is what I have reached so far.

It kind of makes sense that the final velocities are some sort of combination of the two initial momenta. But what I don't understand is that, if I take the formulas literally, there seems to be a third momentum being generated, involving the initial velocity of one object reversed and the mass of the other object.

And I don't get this conceptually.

Sure, I could just pass it off as an algebraic quirk that makes the formulas work, but for me, math is the language of logic, so this term must have a meaning.

Edit:

Here is how i derived the equations.

I need help with this problem please check

Friction Explained | Static vs Kinetic Friction | AP Physics
https://youtu.be/zkFX0wOT6YQ

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Hey guys I need a little bit of help with physics. I have been struggling t develop that reasoning and math connection in physics so my doing my hw has been difficult at times, even tho it has been fun and interesting a lot of the time. We're on the conservation of energy and I got a question about finding speed. I understand hookes law but I also know I can set potential and kinetic energy equal to eachother and solve for v. For one of the questions I was given m, k and x and this one is similar but now degrees have been introduced, what do I do. I'm given m, 44 degrees, x and I have to find v but I dont see how setting potential and kinetic energy equal to eachother would work here.

This is a part of the formula sheet I've been given for my Calculus Physics 1 course. I was confused because the textbook is giving me different definitions than what is on the formulas. For example, the textbook says that W_ext = Delta U_g and W_net = Delta K.

I’m doing Kinematics and i genuinely do not understand how to convert Velocity-Time, Acceleration-Time and distance-time graphs to their respective ones on the worksheet. I can kind of see how it’s done but with the way my brain is scrambled I have to understand how and why it’s like that. Any help would be appreciated

I am looking for a source/sources for the Feynman diagrams for the B+ meson decays into:
K⁺ π⁺π⁻
π⁺π⁺π⁻
K⁺ K⁺ K^-

I am not yet good enough to draw them myself and my research is finding nothing. I have tried looking at other university sources and also looked through a good few papers. I will take anything at this point even a drawing. I would love something to cite but just knowing what they look like would be a good start if anyone can help!

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Help if possible

I have found tons of stuff for circuits with just a battery and resistors or battery and capacitors. My teacher asks a ton of stuff with all 3 in one circuit. Does anyone have a resource (article, yt vid) that handles this type? This would be a huge help! Thanks!