1. Gravitational Force and Distance:
* Inverse Square Law: The force of gravity between two objects is inversely proportional to the square of the distance between their centers. This means that as the distance between the objects increases, the gravitational force decreases rapidly.
* Earth's Radius: The Earth is huge! Its radius is approximately 6,371 kilometers. Compared to this, a few hundred meters is a tiny fraction.
2. The Effect of Distance on Acceleration:
* Since the distance between the falling object and the center of the Earth changes very little within a few hundred meters, the gravitational force acting on the object remains almost constant.
* Constant force means constant acceleration.
3. Air Resistance is the Bigger Factor:
* While gravitational acceleration is nearly constant within a few hundred meters, air resistance becomes a much more significant factor as an object falls.
* Air resistance increases with speed, so it can have a significant impact on the object's acceleration, especially over longer distances.
Example:
Imagine a ball dropped from a 500-meter tower. The change in distance from the Earth's center is negligible compared to the Earth's radius. Therefore, the gravitational force, and thus the acceleration due to gravity, remains almost constant throughout the fall.
Conclusion:
While technically, gravitational acceleration varies slightly with distance, for objects falling a few hundred meters near the Earth's surface, this variation is so small that we can consider it constant for practical purposes. Air resistance, on the other hand, can have a more noticeable impact on the object's motion.
