Projectile motion

Welcome! I am excited to help you master the physics of things flying through the air. Before we dive into the math and diagrams of projectile motion, I would love to know a little bit more about you so I can tailor our conversation perfectly to your needs.

To help me customize our session, could you let me know what your current experience level with physics is (e.g., high school, college, or self-study) and if you have a specific goal, such as preparing for an exam or just learning the concepts?

I have zero physics background and want an easy introduction

To kick off our journey, let's start with the absolute simplest definition. A projectile is any object that you launch, throw, or drop into the air, which then moves under the single, lonely influence of .

Think about tossing a set of keys to a friend across the room. The moment those keys leave your hand, they are in a state of . No rocket engines are attached to them, and there is no steering wheel. Only gravity is pulling them downward while their own momentum carries them forward.

To make things beautifully simple in introductory physics, we always ignore air resistance. Because of this, things like a kicked soccer ball, a launched cannonball, or a dropped rock are perfect projectiles. A flying bird or a soaring rocket, on the other hand, are not projectiles because they use wings or engines to fight gravity.

Let's continue to the independence of horizontal and vertical motion.

Let's explore one of the most mind-blowing, counterintuitive secrets of the universe: horizontal and vertical motion do not care what each other are doing.

Imagine you are standing on a flat field. In your left hand, you hold a red ball. In your right hand, you hold a high-powered spring launcher with an identical blue ball. At the exact same microsecond, you do two things: you drop the red ball straight down, and you fire the blue ball perfectly horizontally.

Which ball do you think hits the ground first? Because the horizontal forward motion and the vertical downward motion are completely , they both pull toward the Earth at the exact same rate. Gravity only cares about pulling things straight down; it does not care how fast an object is flying sideways.

A motion study showing a red ball in vertical free-fall and a blue ball in projectile motion, aligned at six identical time steps by horizontal dashed lines.

I've started generating a visual simulation above to show you this side-by-side. As you will see, even though the blue ball flies far to the right, both balls stay perfectly level with each other the entire way down and clack against the floor at the exact same millisecond.