Two
objects with masses m1 and m2 and initial
velocities v1 and v2 (because this example is a
1-dimensional problem, we have again omitted the vector arrows)
collide elastically. What are their final velocities, v3
(for object 1) and v4 (for object 2)?
Answer:
The total momentum is always conserved in collisions. And because this collision is elastic, by definition total kinetic energy is also conserved. This means we have 2 equations for 2 unknowns, leading to:
v4 = v1 (2m1)/(m1+m2) + v2 (m2-m1)/(m1+m2)
These
equations are the general solution for all one-dimensional
elastic collision problems.