Question

Two objects of mass m move in opposite directions toward each other. The green object moves at velocity v, and the blue object moves at velocity 2v. Which diagram correctly shows the direction and velocity for each of the objects after an elastic collision?

A diagram of two blocks. The block on the left is labeled m with a velocity vector to the left, labeled v. The block on the right is labeled m with a velocity vector to the left, labeled 2 v.

A diagram of two blocks. The block on the left is labeled m with a velocity vector to the right, labeled 2 v. The block on the right is labeled m with a velocity vector to the right, labeled 2 v.

A diagram of two blocks. The block on the left is labeled m with a velocity vector to the left, labeled 2 v. The block on the right is labeled m with a velocity vector to the right, labeled v.

Answer 1

The third diagram.

For equal masses in a 1D elastic head-on collision they simply exchange velocities. If we take right as positive and the left object’s initial velocity u1 = +v and the right object’s initial velocity u2 = −2v, then the final velocities are v1 = u2 = −2v (leftward at 2v) and v2 = u1 = +v (rightward at v). Momentum and kinetic energy are conserved.