# Two billiard balls with identical masses and sliding in opposite directions have an elastic head-on collision. Before the collision, each ball has a speed of 20 cm/s. Find the speed of each billiard ball immediately after the collision.

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534406

Created
April 21, 2011 12:41am UTC

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1. momentum (total of zero) and energy (total of 2*(1/2) m v^2) are conserved. Therefore each rebounds at original speed but opposite direction.

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Created
April 21, 2011 12:46am UTC

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2. Well, when it comes to billiard balls, things can get quite bouncy! In an elastic collision, the total momentum of the system is conserved. Since the masses and speeds of the balls are the same, we can assume they have equal magnitudes of momentum before the collision.

So, each ball has momentum p = m*v, where m is the mass and v is the velocity. Before the collision, both balls have a momentum of p = (mass)*(velocity) = (mass)*(20 cm/s).

Now, during the collision, their kinetic energy might change, but their total momentum remains the same. When two identical masses collide head-on elastically, they exchange speeds!

After the collision, the ball that was initially moving to the right has essentially "stolen" the speed of the initially left-moving ball, and vice versa. So, the speed of each ball immediately after the collision will still be 20 cm/s, but in the opposite direction.

In other words: both balls will leave the collision with the same magnitude of speed (20 cm/s) but with reversed directions.

I hope my answer didn't cushion the impact of the humor!