Let two bodies push on each other and nothing else does. Newton's third law makes their forces equal and opposite, over the same contact time, so the impulses are equal and opposite too: whatever one body loses, the other gains. Add them up and the total never moves. That is conservation of momentum: $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$, read aloud m-one u-one plus m-two u-two equals m-one v-one plus m-two v-two.

The subscripts, once, in words: the number names the body — 1 is the first, 2 is the second — and the letter names the time, $u$ before the collision and $v$ after. So $m_1$ is the first body's mass in kilograms, $u_1$ its velocity before in m/s, $v_1$ its velocity after; $m_2, u_2, v_2$ say the same for the second body. Five of those six are given and the sixth is your answer. Two disciplines make it work. Signs: declare a positive direction in your first line, and anything moving against it enters negative — a dropped minus on a head-on collision is the most expensive keystroke in this chapter. Scope: momentum is conserved in every collision, gentle or catastrophic. Kinetic energy is not, which is the next two lessons.