The complexities of falling freely
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908279896014848 |
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| author | Sen, Anindya Chebolu, Sunil |
| author_facet | Sen, Anindya Chebolu, Sunil |
| contents | 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? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The complexities of falling freely Sen, Anindya Chebolu, Sunil History and Overview 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? |
| title | The complexities of falling freely |
| topic | History and Overview |
| url | https://arxiv.org/abs/2503.17889 |