Hey, guys. For the next couple of videos, we're already talking about projectile motion. This is a super important topic in physics you absolutely will need to know how to solve problems for. Now there's a lot of different variations of problems in projectile motion and it might seem that there are different ways to solve them. So what I'm going to show you in this video is I'm going to introduce the main types of projectile motion that you'll see, and I'm going to show you that to solve them, we're just going to use equations that we've already seen before. So let's check it out.

Projectile motion is going to happen whenever you take an object and you throw it, and it moves in 2 dimensions, that's the important part, under the influence of only gravity. So we've actually seen something similar to this before when we studied 1-dimensional vertical motion. If you take an object and you throw it straight up, then it comes straight back down along the same direction that you threw it, because it's under the influence of only gravity. It just moves purely up and down.

What's different about projectile motion is that we're not going to throw something up and down. We're going to give it some sideways velocity, whether we're throwing it perfectly horizontal, downwards, or upwards. These are really the main types that you might see. But because we're giving it some sideways velocity, it doesn't just go up and down. Instead, it goes to the side while also falling because, just like in vertical motion, it's still under the influence of only gravity.

So because it's moving sideways and up and down, it takes these 2-dimensional parabolic paths. Some other examples that you might see are where you throw something downwards or even upwards. So you might see situations where it returns to the same height, or it might go even to a lower height or even a higher height like this. But this is really it. These are all the different kinds of variations that you might see. All of your problems are going to fall into one of these categories.

So what's common through all of them is that the acceleration, and the only thing that's influencing this object, is just gravity that acts vertically downwards. So we have these 2-dimensional parabolic paths. So how do we solve problems? Well, remember, whenever we have physics problems in 2 dimensions, whether it's motion or vectors, we can always decompose them into 1-dimensional x and y parts, and it's no different for projectile motion.

So what we can do here is we can kind of break up this motion, this parabola into the x and y axis here. So imagine that we have this object here, let's call this point A, and it moves to the ground which is point B. And if we could only move along the x-axis, then what it would look like is even though this is taking a parabolic path like this, in the x-axis, this object just moves from a to b like this. Now it's also moving in the y-axis. So from a, it's also falling under the influence of gravity like this.

So it's really just doing two of these motions, at the same time, and that's why it looks like a parabola. We can actually do this for any other motion. I'm just going to pick one over here. So like for instance, from a, and then it goes up to some point. Let's call that B. Then it goes back down again. Let's call that point C. We can just take this and break it up into its two one-dimensional parts in the X and Y. So if you only could move along the X-axis, then in the X-axis, you would just go from a to b to c like this.

In the Y-axis, if you could only move along the Y-axis, what this projectile would look like is it would go from a and then it would go up to b, and then it would go back down to c. So it would actually look a little bit like this motion over here. So really, it's just these two one-dimensional motions that are happening at the same time. Now why is this important? Because we take a look here, the only acceleration that this object experiences is just going to be in the Y-axis due to gravity.

So when it comes to these two one-dimensional motions, projectile motion is really just a combination of horizontal motion where the acceleration in the x-axis is equal to 0 and vertical motion where the acceleration in the Y-axis is equal to negative g. It's negative because we're always going to assume that up into the right is positive, and g acts downward, so it's negative.

Now why is this important? Because when it comes to the equations that we use for projectile motion, we're really just going to be using combinations of motion equations and vector equations. Now if the acceleration in the x-axis is equal to 0, that actually simplifies a lot of our four equations here because the acceleration terms will go away, and these equations actually aren't really helpful to us. In the third term, the acceleration term goes away, which means that the only equation that we're going to use in the x-axis for projectile motion is just our equation for constant velocity.

Now in the Y-axis, where you have some acceleration that isn't equal to 0, and it's actually equal to negative g, then we're just going to use our three to four equations of motion, and that's really it. And the other thing is because we're moving from one to one dimension to 2-dimensional motion, we're also just going to need some general vectors equations. That's really it, guys. There's nothing new that we haven't already seen before how to do. So let's go ahead and take a look at how to solve some problems.