# Projectile motion without calculus

## TL;DR

This paper introduces a novel algebraic and geometric approach to analyze projectile motion, avoiding calculus and providing educators with an alternative teaching method for complex problems.

## Contribution

It presents a new non-calculus method using travel times to analyze projectile motion, expanding teaching techniques in introductory physics.

## Key findings

- Provides an algebraic-geometric framework for projectile analysis
- Offers an alternative method for complex projectile problems
- Enhances teaching strategies without calculus

## Abstract

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary techniques, which can hardly be assumed of the targeted audience. In the literature, several attempts have been undertaken to avoid calculus altogether and keep the exposition entirely within the realm of algebra and/or geometry. In this paper, we propose yet another non-calculus approach which uses the projectile's travel times to shed new light on these problems and provide instructors with an alternate method to address them with their students.