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Assume there are 2 balls on the table. Cue ball and another ball. What is the angle at which the cue ball should hit another ball for it to go in?

IamH1kc
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  • Perhaps a duplicate of http://physics.stackexchange.com/questions/6646/physics-of-simple-collisions? – David Z Nov 07 '11 at 06:50

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To the extent that it is an elastic collision (and it is, to a good approximation), at the moment of impact, the cue ball, the other ball, and the target pocket should form a straight line. So you should aim the cue ball such that when it touches the other ball the centers of the balls line up with the cup.

The reason for this is that when frictionless spheres contact each other the only force they can exert on each other is directly away from each other. Since the target ball is at rest, whichever the direction of force is pointing is the way it will go.

Mark Eichenlaub
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Rex Kerr
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  • It won't go in if the ball is placed right in front of a rail. The ball would keep hitting the opposite rails. As there is no friction, there wont be any change in angle thus the ball would keep hitting the opposite rails till it comes to rest. – IamH1kc Nov 07 '11 at 06:49
  • Sorry I voted -1. I misunderstood your answer. I thought you were saying that the two balls and the pocket had to be lined up. Now I see you are saying that the cue ball is hit such that when it touches the other ball they need to line up with the pocket. You are right. My down vote is locked but if you edit the answer I will remove my down vote. Sorry about that.... – FrankH Nov 07 '11 at 07:14
  • @Frank: you can always propose an edit yourself to clarify the answer, and (once it is approved) it would give you the ability to remove your downvote as a side effect. – David Z Nov 07 '11 at 08:00
  • Up-voted to remove the -1. (If there is no friction, there will be no rolling, correct? Linear momentum should be conserved.) – Antillar Maximus Nov 07 '11 at 13:46
  • @Rex I hope you don't mind the edit. I, and apparently several other people, found the original wording misleading. – Mark Eichenlaub Nov 07 '11 at 14:34
  • @MarkEichenlaub, Thanks for the edit so I could change my -1 to a +1. – FrankH Nov 07 '11 at 17:01
  • @IamHiccup, if the target ball is touching a rail it is still possible to hit it with the cue ball so that the target will go right along parallel to the rail without bouncing off the rail and it will go into the pocket at the corner. Do you still have a problem with this answer? – FrankH Nov 07 '11 at 17:03
  • So, if the ball is at an angle x from the hole, 90-x should be the angle at which the cue ball should meet the other ball for the ball to go into the pocket, right? – IamH1kc Nov 07 '11 at 18:21
  • No, I was wrong. This is my proposed answer: http://pastebin.com/m4Vbxfa5 – IamH1kc Nov 07 '11 at 18:41