Alright, so today we've got another problem. And in this case we got a child sitting on a rolling chair holding a fire extinguisher and they've got a combined mass of 85 kilograms and is moving at 3 meters per second. Okay, and if a kid needs to be moving at 6 meters per second in order to win this rolling chair race, it's a lot on the line here, he's looking for gold, then how much of this gas you need to shoot out if the gas is released at 25 meters per second. Alright, so this is what we know and we can kind of get rid of some of this in just a minute, but specifically we want to make sure that we know what we're looking for is what's the mass of this gas, the mass the gas. So let's write some things down. The first thing that I'm going to write down here is actually we've got this total mass and that's going to be the mass of the student, the chair and the fire extinguisher with all of the gas inside of the fire extinguisher. And what we need to know is also keeping track of some of these science positives and negatives. And so we're going to start off by doing our big conservation of momentum equations that we've now know and love. Alright, so here we go, I've got some of the things in green that it referred just to the student, things in black that refer to the student and the gas, things that are in blue are just the gas. So let's start figuring out some of these numbers, plugging some things in. The first thing that you might notice is we don't have the mass of the student and we don't have the mass of the gas. We don't have either of these. The only thing we have is the total mass. So we're going to need one more equation to get things kicked off here. And that's the relationship that we need. We've got something that tells us that the total mass is 85 kilograms. That means that the mass of the student and the chair and the leftover gas, so that the leftover mass that's moving to the right at the end of the problem, plus the amount of gas that we shoot off to the left, is going to be equal to this total amount of 85 kilograms. And so we can actually go through and replace some of these numbers in our equation with each of those. So the big thing to notice here, I rewrote this so that it was in terms of ms the mass of the student because that's not what we're trying to calculate. And we have two unknowns in this equation. We know the initial velocities both at these and the final velocities of each of these, but we don't know either of the masses. So we needed a second equation to relate the two, so we had two equations, two unknowns. We can now take this here and plug it back in for the mass of the student here and here to get this expression. To get this, however, you might notice on this side that we've got mg times vi with the negative sign and mg times vi with the positive sign. And the reason why at the beginning, everything's moving all together so we can just treat it like it's 85 kilograms moving all together to the right because that's what we've got in this situation. So we plug it in, we get here 85 times 3 on the left hand side. We're going to plug in the numbers on the right hand side too and then we're going to go back and try to solve for this mg. Now that we've got everything plugged in, we're going to have to distribute a little bit and combine like terms. We don't need this anymore now that we've sort of already plugged it in. So we are going to finish up combining like terms and then solve for the mass of the gas. Here we go, dividing both sides by 31 meters per second. And we get that the mass of the gas is 8.226 kilograms. And so if we look through, went back to our original equation and plugged everything in, the masses and velocities that's 85, the total mass times 3 meters per second, that number that you get there, if you want to go back and check, should be equal to the mass of the student left over, which is going to be 85 minus 8.226 times 6 meters per second, plus this 8.226 times negative 25 meters per second because that gas is shooting in the other direction. If we think about it, this is actually the way that rockets work. They shoot off their fuel in the opposite direction that the rocket goes because in space there's nothing to push against to cause you to have a momentum to change your momentum. Just like if you were floating in space, all you could do is throw something in one direction so that you go the other way. That's it for this one. We're going to be doing more problems like this in class where we've got to do calculations a little more complicated, add something else on it, like a friction, maybe do some of these combined mass. So we'll see you in class.