Final answer:
The mechanical energy of the prisoner will be the sum of the kinetic energy J and the potential energy, which is J times greater than the kinetic energy, resulting in a total greater than J + J^2. The exact total cannot be determined without the specific value of J.
Step-by-step explanation:
The question asks about the prisoner's mechanical energy when their potential energy is J times greater than their kinetic energy, J. The mechanical energy (ME) in a system is the sum of its potential energy (PE) and kinetic energy (KE). Given the potential energy is J times greater than the kinetic energy, we can express this as PE = J × KE. Since we know KE = J, then PE = J2. The total mechanical energy is the sum of PE + KE, which is J2 + J. Without the specific value of J, we cannot determine the exact numerical value, but conceptually, the mechanical energy is J + J2, which is greater than any of the options provided (2J, 3J, 4J, 5J).