Why on Earth is Gravity Positive?!

So you're working hard on your physics homework and you go to check your answers. You notice the answer key has your same answer... But with the opposite sign. What's the deal with that? Gravity is always negative, isn't it? Positive gravity? Why?! How?! Well young physics student, you are forgetting a very important physics rule: always define your coordinate system!

Huh? What's that?

The coordinate system defines the cardinal directions of your problem. They are typically labelled as x, y, and z with the direction of the arrow indicating the positive direction. In your math courses you pretty much always see it like this:

However, in physics you are free to define the directions in anyway you see fit. This means you can define your coordinate system in such a way that the signs and numbers are simple. So you might end up with a coordinate systems like this:

Okay, but what does this have to do with positive gravity? Let's look at an example!

You are standing on a cliff and kick a ball off of it. It free falls for 8 seconds. How far has the ball fallen?

Some textbooks have a negative sign in front of the gravity term and make you memorize that it is for a specific coordinate system and that gravity is always positive, yada yada yada. I find it much easier to pay attention to your coordinate system and keep all the terms in the formula positive. Your numbers will work themselves out and makes you think about what's going on.

Good luck on the rest of your homework!