A child runs in a straight line tangent to a playground carousel, jumps on, and holds tight as the carousel begins to rotate. Which of the following statements is correct for this collision?

(a) The coefficient of restitution is greater than 1 because there is now rotational energy where there was none before.

(b) The coefficient of restitution is 1 because the system's translational kinetic energy is completely converted to rotational kinetic energy.

(c) The coefficient of restitution is less than 1 because the sum of the translational and rotational kinetic energies in the final state is less than the sum in the initial state.

(d) The coefficient of restitution cannot be defined in a system in which there is both translational motion and rotational motion.

(e) Explain why all the answers except the one you chose are wrong.