Final answer:
The d. change in potential energy of a ball dropped from an eleven-story building to a ninth-floor balcony is the same regardless of where the zero point (y = 0) is set, due to the conservation of mechanical energy.
Step-by-step explanation:
When considering the change in potential energy of a ball dropped from the top of an eleven-story building, the reference point for measuring potential energy is arbitrary. That is, it doesn't matter where we set the y = 0 level; it could be at the ninth floor balcony, the ground level, or the top of the building. The key point is that the change in potential energy depends only on the vertical distance the ball travels, not on the choice of the zero level. Therefore, the change in potential energy is the same in all three cases (a, b, and c).
The initial potential energy is at its maximum when the ball is at the top, and it decreases as the ball falls towards the ninth floor. This is in accordance with the principle of conservation of mechanical energy, which states that when ignoring air resistance and other non-conservative forces, the sum of potential and kinetic energy remains constant.