The complexities of falling freely
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?
Cite
@article{arxiv.2503.17889,
title = {The complexities of falling freely},
author = {Anindya Sen and Sunil Chebolu},
journal= {arXiv preprint arXiv:2503.17889},
year = {2025}
}
Comments
8 pages, to appear in The College Mathematics Journal