 you're stuck inside, doesn't mean you can't have any fun. If for you fun is solving roller coaster problems. Let's take a look at this roller coaster problem. Here we have the roller coaster moving three meters per second, 15 meters up in the air to start off with. Later on it's going to be seven meters up in the air and we want to know how fast it's going at that point in time. We're going to start these types of problems off by labeling on our diagram the type of energy present at each point. So at the top of the hit first hill there is both gravitational potential and kinetic energy. Gravitational potential because it's some height in the air and kinetic because it's moving. And at the top of the second hill there's also gravitational potential and kinetic energy because it's moving and it has some height up in the air. Now the key to any of these conservation of energy problems is that the total energy at any two points on the movement of the object is going to be equal. So we can figure out the total energy at those two points. We can make them equal to each other in an equation and we can go through and solve. So on the left hand side of the equation I've said EP plus EK. That's because to start off with at the top of the first hill there was both gravitational potential and kinetic energy. On the right hand side I have EP plus EK again. Those were the types of energy at the second hill and they're equal to each other. Now I'm going to substitute in for EP, MGH in both the positions and for kinetic energy one half MV squared in each of the positions. Now there's a mass in each of those four terms and I can cancel that mass out and now I've got a little equation I can substitute some numbers into. On the left hand side I've put in three meters per second for the speed of the roller coaster as it started off the top of the hill and I put in a height of 15 meters because it started off 15 meters up. On the right hand side I left the V blank that's what I'm trying to find the speed at the second hill and I put in the height of the second hill as well. Here's how I put it through my calculator. I enter in all of the left hand side first then I subtract the GH term from the right hand side. That way I only have the one half V squared. Then I'm going to multiply both sides by two and I'm going to square root to get V by itself. That's going to give me a speed of 13 meters per second at the top of the second hill. Check out my channel for some more videos on solving problems with the law of conservation of energy.