Final answer:
The angle between the velocity vectors of two balls after an elastic collision where one was initially at rest is 90°. Since one ball is deflected by 30°, the other will be deflected by 60° relative to the original path. Conservation of momentum and kinetic energy confirms the elasticity of the collision.
Step-by-step explanation:
The question relates to elastic collisions in two dimensions, where two objects of equal mass collide, and one is initially at rest. To solve for the angle between the velocity vectors of the two balls after the collision, we can use the conservation of momentum and the fact that for elastic collisions of objects with identical masses, the angle between their final velocity vectors is always 90°. Since the cue ball is deflected by 30°, the second ball will be deflected by 60° from the cue ball's original path to satisfy the 90° separation.
To confirm that the collision is elastic, we also need to ensure that both the kinetic energy and momentum are conserved. For an elastic collision involving equal masses where one is initially at rest, the incoming object will transfer all of its momentum to the other object if it comes to rest after the collision. However, if the incoming object continues moving but changes direction, then the angles of deflection will ensure that the momentum is still conserved, and by the nature of elastic collisions, so is the kinetic energy.