Yes, the rate at which objects fall does change with location and altitude on Earth due to variations in the acceleration due to gravity. The acceleration due to gravity is not constant everywhere on Earth's surface, primarily because the Earth is not a perfect sphere and its mass is not uniformly distributed. Additionally, factors like altitude, latitude, and local geology can influence the acceleration due to gravity.
Near the surface of the Earth, the average acceleration due to gravity is approximately 9.8 meters per second squared (m/s²). This value is often rounded to 9.8 m/s² for simplicity. However, this value is an average and can vary slightly depending on the location.
At different altitudes, the distance between an object and the Earth's center changes. As a result, the gravitational force acting on the object decreases slightly with increasing altitude. This means that objects will experience a slightly weaker acceleration due to gravity at higher altitudes compared to sea level. However, this change in acceleration is relatively small and is not easily noticeable in day-to-day life.
It's worth noting that other factors can also influence the rate at which objects fall, such as air resistance or buoyancy in the case of objects submerged in fluids. These factors can further complicate the behavior of falling objects, especially at different altitudes or in different atmospheric conditions. However, in the absence of significant air resistance or other factors, the gravitational acceleration will be the primary determinant of how fast objects fall.