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HI! i have a project for physics and we have to talk about billiard balls, more specifically, 8 ball pool. if our project, one topic

HI! i have a project for physics and we have to talk about billiard balls, more specifically, 8 ball pool. if our project, one topic is 2 dimensional elastic collision, We have not learned this yet and i have read only briefly. to my knowledge there seems to be two different elastic collision examples, one in which the cue ball hits a stationary ball and they "trade kinetic energy", as in the cue ball then becomes stationary and the other ball receives the cue ball's original kinetic energy. the other example I keeps seeing is one ball hitting another and the two balls diverging into two different directions. I am very confused of which one to use and why they are different. I have attached two photos and would like your help as soon as you can!

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