Final answer:
The velocity of the red billiard ball will be 4 m/s when the cue ball stops, and 2 m/s when the final velocity of the cue ball is 2 m/s after an elastic collision.
Step-by-step explanation:
When a cue ball collides elastically with another billiard ball, we use the conservation of momentum and the conservation of kinetic energy to determine the velocities after the collision, because in elastic collisions both momentum and kinetic energy are conserved.
For the first scenario where the cue ball comes to rest post-collision (final velocity is 0 m/s), all of its momentum is transferred to the red ball. Therefore, using conservation of momentum:
mcue × vinitial cue = mred × vfinal red
Given that both balls have the same mass, 0.35kg, and the initial speed of the cue ball is 4 m/s, then:
0.35kg × 4 m/s = 0.35kg × vfinal red
The velocity of the red ball will also be 4 m/s.
For the second scenario where the cue ball's final velocity is 2 m/s, we have:
0.35kg × 4 m/s = 0.35kg × 2 m/s + 0.35kg × vfinal red
Therefore, the velocity of the red ball in this case will be:
vfinal red = (0.35kg × 4 m/s - 0.35kg × 2 m/s) / 0.35kg = 2 m/s
Hence, the red ball's velocity will be 2 m/s.