Final answer:
The energy at position P is equal to the energy at position Q because the total mechanical energy of the arrow, including both potential and kinetic energy components, remains constant throughout its trajectory, assuming no external work is done.
Step-by-step explanation:
Regarding the energy of an arrow at positions P and Q, without specific information provided about what these positions represent, the most likely interpretation is that they refer to different points in the arrow's trajectory. According to the principles of conservation of energy and the work-energy theorem, the total mechanical energy of the system (arrow on its flight path) remains constant if we ignore air resistance and other non-conservative forces. Thus, the sum of potential energy (U) and kinetic energy (K) at any point in the arrow's trajectory will be equal to the arrow's total mechanical energy (E).
If position P represents the highest point in the trajectory, the arrow will have maximum potential energy and minimum kinetic energy, and at position Q, if it is at a lower point, it will have lower potential energy than at P and consequently higher kinetic energy. Given these conditions, the correct statement is that the energy at position P is equal to the energy at position Q because the total mechanical energy remains constant throughout the flight of the arrow.