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# Two billiard balls of equal mass undergo a perfectly elastic head-on collision. if the speed of ball 1 was initially 2.00 m/s, and that of ball 2 was 3.00 m/s in the opposite direction, what will be their speeds after the collision? ball 1

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The collision is elastic, this means that both the total momentum and the total kinetic energy is conserved after the collision.- Let's start with the conservation of the moment:Let's take as positive the direction of the initial direction of the ball 1. We will label with m the mass of the balls (that have the same mass), the final velocity of the ball 1, the final velocity of the ball 2. The initial speed of ball 1 is 2 m/s, while the initial speed of the ball 2 is -3 m/s (with a negative sign, because it's going in the opposite direction to that of the ball 1). The conservation of momentum becomesFrom that we are - now Let's write the conservation of kinetic energy:that becomesSubstituting as we have found in the conservation of momentum, and simplifying, we getwhich has two solutions: (1) (2)The second solution is meaningless: in fact, the balls have exactly the same speed and direction as before the collision. This would mean that they are not found at all, so that we can neglect the solution 2. And so, the solution of the problem (1).