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I am doing an experiment where I need to know the final velocity of the blue ball after the collision. With this knowledge, I can scale this experiment down to the atomic level and have a general knowledge of what will happen to protons. Is the final velocity just 3cos(45) + 3? If not, what is the final velocity of the blue ball, and what is this type of problem called? Also, can this method also be applied to the atomic level or is the way momentum dealt with at the atomic level different?

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look it up in wiki, https://en.wikipedia.org/wiki/Elastic_collision the part with two dimensional collision-

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