Final answer:
The change in gravitational potential energy of the pole is calculated using the formula ∆PE = mgh, considering the pole's center of gravity at the middle of its length.
Step-by-step explanation:
To calculate the change in gravitational potential energy of the pole as it falls, we can use the formula ∆PE = mgh, where m is the mass of the pole, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height. Since the pole is balanced vertically and then falls, its initial height can be taken as the distance from its center of gravity to the ground, which is half its length (1.7 m). The change in potential energy will be from this height to zero when it hits the ground. Substituting the given values (m = 12.60 kg and h = 1.7 m) into the formula gives ∆PE = 12.60 kg × 9.81 m/s² × 1.7 m, which calculates the change in potential energy.