When two objects with the same mass are dropped from the same height, they may not reach the ground at the same time due to several factors, primarily involving air resistance (drag force) and the object's shape and surface area.
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Air Resistance: As objects fall through the atmosphere, they encounter air resistance, which acts in the opposite direction to their motion. This force depends on the velocity of the object, its surface area, and the density of the air. If two objects have different shapes or surface areas, they will experience different amounts of air resistance. For instance, a flat piece of paper will fall slower than a crumpled piece of paper due to greater air resistance acting on the larger surface area of the flat paper.
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Shape and Surface Area: The way an object is shaped can significantly affect how it interacts with air resistance. For example, a feather and a metal ball dropped from the same height will fall at different rates not because of their masses but because of how their shapes affect drag. The feather's larger surface area relative to its mass leads to greater air resistance, causing it to fall more slowly.
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Initial Conditions: If the objects are dropped with any initial velocities or conditions (such as one being dropped straight down and another being thrown at an angle), this will also affect the time taken to reach the ground.
In a vacuum, where there is no air resistance, all objects fall at the same rate regardless of their mass or shape, and they would hit the ground at the same time when dropped from the same height. However, in an environment with air, these factors can lead to differences in fall times.
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