Final answer:
When one ball stops and the other bounces back at half its initial speed after colliding with a wall, momentum may be conserved considering the whole earth-wall system, but kinetic energy is not conserved due to the change in speed.
Step-by-step explanation:
The scenario described involves two identical balls hitting a wall with the same speed. After the collision, the kinetic energy of the balls changes; Ball 1 stops and therefore has no kinetic energy, whereas Ball 2 bounces back with half of its initial speed and hence has less kinetic energy than before. This implies that kinetic energy is not conserved in either case.
As for momentum, it is a vector quantity, which means direction matters. When Ball 1 stops, it loses all its momentum. Ball 2 bounces back with half its initial speed in the opposite direction, indicating a change in momentum. However, if we consider the wall-earth system, momentum may be conserved if the momentum transferred to the earth (through the wall) is accounted for, but typically when discussing the ball and wall alone, momentum does not appear conserved because of the change in the ball's momentum direction and magnitude. Therefore, the correct answer to the student's question is b. Momentum is conserved, assuming the interaction with the wall and earth as part of the system, but kinetic energy is not conserved due to the changes in speeds.