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A physics student leans out of the fortieth story of the physics building and drops two balls of the same size at the same time. One is 0.8 kg and made of iron, and the other is 1.2 kg and made of lead. Not only do the two balls hit the ground at the same time, the heights of the two balls match all the way down.
This somewhat counterintuitive result is an example of a general principle: If air resistance is negligible, then an object in free fall at the surface of the Earth has a downward acceleration of g = 9.8 m/s2. Free fall means that only the force of gravity is acting on an object.
In the following questions, consider a ball dropped from the fortieth story of a building, and consider "down" to be in the positive direction. Consider air resistance negligible unless noted otherwise.If an object falls a distance Δx during the first t seconds, how far does it fall during the first 3t seconds?