Yes, an object falls at the same rate regardless of its horizontal motion. This is because the acceleration due to gravity is the same for all objects, regardless of their mass or velocity.

Objects in free fall accelerate at a constant rate of 9.8 meters per second squared (32 feet per second squared) on Earth. This means that their speed increases by 9.8 meters per second (32 feet per second) every second.

Horizontal motion does not affect the acceleration due to gravity. Whether an object is moving horizontally or vertically, it will fall at the same rate.

For example, if two balls are dropped from the same height, one moving horizontally and the other vertically, they will both reach the ground at the same time.