Final answer:
During a jump on a trampoline, a person's kinetic energy is transformed into potential energy as they ascend, and potential energy is converted back into kinetic energy as they descend. The conservation of energy principle implies that the total mechanical energy remains constant during the jump. The correct option describing these changes is option d, 'KE decreases and PE increases'.
Step-by-step explanation:
The question deals with the concepts of kinetic energy (KE) and potential energy (PE) in physics. When a person jumps on a trampoline, their kinetic energy and potential energy transform different phases of the jump. As the person jumps up off the trampoline, their kinetic energy, which is the energy due to motion, is converted into potential energy, which is the energy stored due to their elevated position against gravity. Conversely, as they fall back down, the potential energy is transformed back into kinetic energy. The statement that describes these changes accurately is 'While going up, the person's KE would change to PE. While coming down, the person's PE would change to KE.'
This aligns with the physics principle of energy conservation, where the total mechanical energy (KE + PE) in a closed system remains constant if we ignore external forces such as air resistance and friction. In the scenario of jumping on a trampoline, at the highest point of the jump, the kinetic energy is at its minimum (ideally zero if we momentarily ignore air resistance), and the potential energy is at its maximum. At the lowest point, right before and after the bounce, the potential energy is at its minimum, and the kinetic energy is at its maximum. The given expressions, KE = -APEg = -mgh, indicate the mathematical relationship between kinetic energy and potential energy (where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height). As the height increases, potential energy increases and kinetic energy decreases, due to the negative sign. The correct explanation is that the kinetic energy decreases and potential energy increases when the person jumps upward (option d).