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arXiv · 2503.17889

The complexities of falling freely

Anindya Sen·Sunil Chebolu
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Abstract

Suppose you drop a coin from 10 feet above the ground. How long does it take to reach the ground? This routine exercise is well-known to every AP physics and calculus student: the answer is given by a formula that assumes constant acceleration due to gravity. But what if you ask the same question in the more realistic scenario of non-constant acceleration following an inverse square law? In this article, we explain the analysis of this realistic scenario using freshman-level calculus and examine some implications. As a bonus, we also answer the following intriguing question: Suppose the Earth were to instantaneously collapse to a mathematical point at its center. How long would it take for us surface dwellers to fall to the center?

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Anindya Sen, Sunil Chebolu. 2025-03-23. The complexities of falling freely. https://doi.org/10.1080/07468342.2024.2419794

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