So, this problem should be easy, and I feel pretty silly even asking this question given my physics knowledge:
A particle of mass $m$ is moving along the x-axis with speed $v$ when it collides with a particle of mass $2m$, initially at rest. After the collision, the first particle has come to rest, and the second particle has split into two equal-mass pieces that move at equal angles, $\theta$, with the x -axis. Which statemente correctly describes the speeds of the two pieces?
Apparently, the answer is:
Each piece moves with speed greater than $v/2$
... Meaning that the momentum of each piece of mass $m$ is greater than $mv/2$—so their total momentum is greater than $mv$. How can this be possible? Apparently no one here has a problem with it, and I certainly understand the mathematics used to justify it, but it seems to fly in the face of one of the most basic physical assumptions. Is the assumption here that there's some other force that propelled the two pieces, as if you were splitting a magnet or something?