 go if I drop it from two meters. Oh okay me too. Wait how are you doing that? I'm using the conservation of energy. But I'm using kinematics. If we were to solve this like a kinematics problem then we'd start off by labeling the diagram with things like initial velocity equals zero meters per second since this ball is being dropped and we'd start off by putting in a final velocity that we don't know and we'd have a displacement of two meters. We'd also know that we have an acceleration due to gravity we can use. Based on those variables we would pick the formula vf squared equals vi squared plus 2ad. No time formula. Now since my initial velocity is zero that formula would simplify down to vf squared equals 2ad and if you wanted to sort of rearrange it vf squared vf equals 2ad square rooted. So I could substitute in and I would get 2 times negative 9.81 meters per second squared times negative 2 meters and I have to make that a negative 2 meters because the ball was falling downwards and I would square it to get my final velocity. It would be negative 6.3 meters per second. Now what if I wanted to do it using the conservation of energy? I'd start off by labeling the diagram with the types of energy that are present at each point. When the ball is first dropped it only has gravitational potential energy because it hasn't started moving yet. When the ball hits the ground all of that energy has been converted into kinetic energy because now it's no meters off the ground is no height off the ground. Then I could start in terms of algebra by making the two types of energy equal. This is the law of conservation of energy explaining that these two types of energy in total have to be equal to one another. Now I can substitute in for either side. For gravitational potential energy I put mgh and for kinetic energy one half mv squared. The mass of the ball is the same on either side so that cancels out and if I go ahead and rearrange this I get 2gh all square rooted equals the speed of the ball. That's the same formula I had although it has some different letters when I did it with kinematics which means when I substitute it in I'm going to get a speed of 6.3 meters per second and if I want that to be a velocity I'll have to put the negative sign on myself since energy doesn't deal with negative signs can only tell you the magnitude of the speed. Well what about figuring out how high the ball goes in the air? Can I use conservation of energy for that too? Yeah! Now we have the opposite problem we've got a velocity of 3.5 meters per second initially for the ball we want to know how high up it goes. Well in this situation if we were using kinematics we would think of the final velocity as being zero since the ball will stop when it reaches its highest point. We would use the no time formula again vf squared equals vi squared plus 2ad and we would go through and start to substitute in. Final velocity is zero initial velocity is 3.5 meters per second and I'd square that plus 2 times the acceleration due to gravity which I'll make as a negative times the displacement. If I went through and solved that I would end up getting the displacement to be 0.62 meters up in the air. If we were to do this with the conservation of energy we would again say that we have gravitational potential energy at the highest point and kinetic energy at the lowest point. We'd make those two energies equal to each other through the conservation of energy put an mgh for the gravitational potential energy and one half mv squared for the kinetic energy. Cancel the masses and substitute in. You'll notice as you do this you get a formula that looks a lot like the last one that we were looking at. When I go through and solve I will also get 0.62 meters. But now I want to work out the speed of this pendulum at its lowest point. It's moving on a curved path and all my kinematics equations only work for one dimension. Energy doesn't care about dimensions. Here check this out. Here we have a pendulum problem where the pendulum starts off 0.5 meters up in the air and we want to know how fast it's going at its lowest point. Now this would be a tricky problem to do with kinematics since all of our kinematics formulas only deal with one dimensional motion. They don't really deal with objects which move in a curved path but this is a problem that works great when we're dealing with the conservation of energy. We can label the diagram start off by saying that the energy to start off is all gravitational potential energy as that pendulum bob is 0.50 meters up in the air and that that energy gets converted into kinetic energy. We can do the same kind of calculation we've done in the last two problems. E p equals E k, M g h equals 1 half m v squared, cancel out the two masses and go through and solve for what the speed is going to be. In place of the acceleration due to gravity I can put in 9.81 meters per second squared. I'm not putting in the negative sign because again energy doesn't care about direction or vectors. Put in the height and solve for the speed. This pendulum is going to be moving at 3.1 meters per second.