 Okay, here I am and I'm going to show you really quickly this numerical calculations. This is an open office. I'm going to go fast, but all this stuff is online too. Okay, so I am going to start off, let's say I throw a ball up from y equals zero at three meters per second. So I'm going to write down some stuff, y zero equals three. Units, it doesn't know any units, so you just got to tell it whatever. I'll call it velocity, I'll call it v zero, let's say it's four, I'm sorry, I wanted that zero. Okay, and then I need to know two more things, dt. This is the time interval between each calculation, and then I need the acceleration. Notice here that there are no units. You could put units over here if you want in this next cell, but don't put them here because the spreadsheet only understands numbers, and if you put letters in there too, it doesn't know what's going on. Now for each time step is going to be a row, and so the next step will be the next row and so forth. So I'm just going to put some labels up here, I'm going to call this a t, I'm going to call this y and v. So the first time is zero, so I'm just going to put zero. And the next time is going to be this time plus the dt, the time step. So I'm going to say equal, that means I'm making an equation, and then I'm going to click this cell, see I put a seven, that cell, a seven, and then plus this. Now in here I'm going to add a dollar sign. So what this does is let me go ahead and press return, and it did that, zero plus point one. Now if I grab this little square box in the corner, it's called the fill, if I drag that down then the spreadsheet says I get it, I'm going to now, if you look at the formula up here, take cell a eight, the one before it, plus b three. And it didn't change the three because I put a dollar sign in front of it. If I didn't have that, let's go back up here. Take the dollar sign out, press return, I get the same thing, but now when I pull it down I get something different. Because then it goes, if you look right here, it says oh I get it, you're moving down, so it moved down to b four instead of saying it b three. So let's go back up here and fix this. Get it? Okay. Copy that down one. Okay, at the first time interval, what's the y? Well, that's just equal to this. And again, I don't want that ever to change, so I'm going to put a dollar sign there. It doesn't really matter in this case. And what's the initial velocity? Well, here's the initial velocity. And why am I doing it this way? Well, let's say I have my calculation and I want to re-run it for a different velocity. If I change this to three, it changes. And this actually is going to make it better, trust me. In a later program, I could have calculated the acceleration in this final column, but that's not going to matter in this case because it doesn't change. Okay, after .1 seconds, what's the new position? Now here's where we're going to use the magic. The new position is the old position plus the velocity. Well, I haven't calculated the velocity yet, so I can't use that. So I'm going to cheat. I'm going to use this velocity. It's wrong. If my time's up small enough, it won't matter. So I'm going to say equals the position before it plus this velocity times the time interval, which is this. And again, I need to put that dollar sign there and return. Okay, so after it has .1 seconds moving at four meters per second at a constant speed, that's what I get, which is wrong, but close enough. Now with the velocity, again, I'll say it's equal to the velocity before plus the acceleration, which is this, dollar sign because it doesn't change, times dt, which is this. Dollar sign because it doesn't change. Okay, again, that's wrong, but it's going to be close enough. So now I have all these values for time, position, and velocity. I can just drag it down for as far as I want. Okay? So this, I'm going to show you this gives you better results, but look. How high did it go? Well, here, this is, look, what's the, here, it went one meter, okay? We can check that, we can do an analytical calculation to find out how high it would go and see that this isn't the right answer. But how long was it in the air? Well, that's when it got back down to zero around, somewhere around here, so about .9 seconds. Okay. Let me show you one quick thing. What if I make the time step smaller? I'm going to make it .01. First thing you'll notice is that it doesn't calculate enough. I'm only up to .5 meters, so I need to have more data. I can go down as far as I want. I want to get down to y equals zero. That'll be the full motion. Okay, there, I'm just about there. Okay, there. So this is t, it took .8 seconds to go up and back down. And then the highest point, I can just scroll up here and look for the highest value, here it's somewhere around here, 8.4, about 8.84. So the first calculation wasn't too bad, okay? So you can play around with this, you can make a graph, which I'm not going to show you how to do, because I don't want it to be too long. So there you go. That's a simple numerical calculation in a spreadsheet. It can get more complicated, but that's a great place to start.