When an object is dropped from a height and released, it does fall directly under its center of gravity. The center of gravity of an object is the point where the gravitational force acts on the object and is the average position of its mass. When there is no external force acting on the object, such as air resistance or wind, the object will accelerate downward due to gravity.
However, it may appear that the object deviates from falling directly under its center of gravity due to external factors like air resistance. Air resistance is a force that opposes the motion of an object moving through the air. When an object falls, it experiences air resistance, which can cause it to deviate from a straight vertical path.
The extent to which air resistance affects the object's motion depends on its shape, surface area, and other factors. Objects with large surface areas or irregular shapes are more affected by air resistance and may experience greater deviations from a straight vertical path. In some cases, objects may also be subject to wind or other environmental factors that can influence their trajectory.
Nevertheless, in the absence of any external forces or factors, an object dropped from a height will fall directly under its center of gravity due to the force of gravity acting on it.