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Do billiard balls hurt?

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Put simply, the answer to this question is yes. But here's how I found out:

The other day, I was playing pool in my basement with my brother and, of course, I was looking at something on my phone just as the cue ball was hitting the 9-ball and he applied so much force that the 9-ball bounced off the table and landed right on my foot. It hurt really bad and I still have a large bruise right on the top of my foot.

Well, since a standard billiard table is .762m and we can use acceleration as 10m/s2 and the billiard ball started from rest from the top of the table, the final velocity that the ball hit my foot with was 3.9m/s. Ouch. A billiard ball's mass is .17kg, so the force that it hit my foot with was 17N. Ouch. Needless to say there is a large bump on my foot from the ball and now I will always pay attention the playing pool with my brother since he clearly doesn't understand physics well enough to be able to hit the ball with enough force that it will still move, but not too much force so that the ball won't end up on the ground.:hocky:

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