Question

Two bodies move in a straight line towards each other at initial velocities v1 and v2 and with constant accelerations a1 and a2 directed against the corresponding velocities at the initial instant.

What must be the maximum initial separation lmax between the bodies for which they meet during the motion?

Answer 1

We shall consider the relative motion of the bodies from the viewpoint of the first body. Then at the initial moment, the first body is at rest (it can be at rest at the subsequent instants as well), while the second body moves towards it at a velocity v1 + v2. Its acceleration is constant, equal in magnitude to a1 + a2, and is directed against the initial velocity. The condition that the bodies meet indicates that the distance over which the velocity of the second body vanishes must be longer than the separation between the bodies at the beginning of motion; hence we obtain