Vectors can be tricky things. If I don't explain it well enough, then consult a science teacher or a dictionary. Hear goes nothing.

A vectors is something that has both a length and a direction. For example, the car is moving south at 24 mph. Only on this website, you won't see something in mph. You'll see it in meters per second or kilometers per hour. The reason vectors are important when dealing with the type of problems you'll see here is because I will make a problem saying that a football is kicked at 45 degrees at 10 meters per second. (Sorry, bad run on sentence.) Then I'll ask you to know how far it went before it hit the ground. To do this, you'll have to know how to work a vector.

For starters, draw a picture. It will look something like this.

You then have to break it into component vectors. This means that you'll have one vector at 0 degrees and another at 90 degrees. This will give you you're velocity in the horizontal direction and your velocity in the vertical direction. THESE TWO VECTORS ARE UNRELATED. THEY CANNOT EFFECT EACH OTHER. I WILL ONLY SAY THIS ONCE. THEY CANNOT EFFECT EACH OTHER. Okay, so I said it twice. Sue me. To get component vectors, use your sine and cosine relationships. When you look at the picture above, you'll note that the football kicked at 45 degrees makes a right angle with the horizontal and vertical axes when you take a line down or across from the top of the original vector. Then just make an equation using SOH CAH TOA. I'm sure you've went over it in Geometry. This equation will look something like:

This will give you the velocity in the x direction or how fast it's going in the horizontal direction. To find velocity in the y or vertical direction, simply use sine instead of cosine.

Now that you have the velocity in the vertical or y direction, you can figure out the time that it is in the air. Then take this time and put it in one of the equations using your horizontal velocity (I'll let you figure out which one) and, poof, there's your answer. Now you can master anything...even the dreaded range equation. Okay, so it's not that hard. I had you going though.