# Why is projectile motion parabolic?

Projectile motion is parabolic because horizontal velocity is typically constant and the object's vertical position is only affected by a constant acceleration (assuming constant drag, etc.).

In short, the fundamental motion of a projectile is parabolic because of its associated equation of motion.

is parabola-describing because it is quadratic.

But if you'd like, I can go into more detail about why this works by performing a little integration. Let's start with a constant acceleration,

Let's move on to position:

This is, of course, the equation of motion I mentioned earlier, so it should look familiar to you.

If an object were dropped and fell straight down with no horizontal velocity, the path would not appear to be parabolic; instead, it would resemble a line, even though it is actually a parabola that has been compressed infinitely horizontally. In general, the more the parabola is compressed horizontally, the smaller the horizontal velocity.

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Projectile motion is parabolic because the horizontal and vertical components of motion are independent, and gravity acts only vertically, causing the projectile to follow a curved path.

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