Feathers and hammers do not fall at the same rate when dropped in normal conditions on Earth. In the absence of other factors, such as air resistance, they would fall at different rates due to their different masses and shapes. However, when you observe a feather and a hammer falling at the same rate in a vacuum or in certain controlled conditions, it is because the effect of air resistance has been minimized.
Air resistance is the force exerted by air molecules as an object moves through the air. It opposes the motion and can significantly affect the rate at which objects fall. In the case of a feather, its large surface area relative to its mass creates a significant amount of air resistance, causing it to fall slowly. On the other hand, a hammer, with its compact shape and greater mass, experiences less air resistance and falls more quickly.
In a vacuum or under conditions where air resistance is minimized, such as in the famous Apollo 15 astronaut experiment on the Moon, both feathers and hammers will fall at the same rate. This is because in the absence of air resistance, the only significant force acting on the objects is gravity, and gravity affects all objects equally regardless of their mass or shape. In such a scenario, both objects would accelerate toward the ground at the same rate, following the laws of free fall.
On Earth, where air resistance is present, feathers are significantly affected by it, causing them to fall more slowly compared to denser objects like hammers.