Hey, guys. Let's work out this problem together. So here we have a 2 kilogram ball that's initially 6 meters above the ground. So let's go ahead and take a look at part a here. We want to calculate the change in gravitational potential energy, so that's Δug. We're going to be using this equation right here for 2 different cases. What happens here in part a is that we have this ball that is 6 meters above the ground. So I know that this sort of level right here, this y value is equal to 6. That's my initial. The ball then is going to fall down to another height. It's going to fall down to a height of 3 meters. So here I have y equals my yfinal equals 3. What I want to do is I want to calculate the change in gravitational potential energy. So you've lost some height and therefore you've lost some gravitational potential energy. So how do we calculate this? Well, what happens is we're just going to use mg×Δy. But what happens in energy problems is gravitational potential energy is always calculated relative to an arbitrary reference point. What happens in part a is that we're choosing the ground, which is y equals 0, to be where the gravitational potential energy equals 0. So what we're doing here is we're saying if this is 6 and this is 3, the ground level is y equals 0 and this is where ug is equal to 0. Notice if you plug in 0 into this equation here, you're just going to get 0. So what happens is we can actually just choose our ground level to be wherever we want. So what happens? We're going to calculate the Δu which is going to be mg×Δy, but I'm actually going to write it out in the longer way. So I'm actually going to write it out as mgyfinal-yinitial. That's what Δy means. So what happens? We're going to get a mass of 2. We're going to have a g of 9.8 and then my final minus initial is going to be 3 minus 6. I'm ending up lower than I started so I should get a negative number here. So I get 3 minus 6. When you plug this all in you're going to get negative 58.8 joules. This makes sense that you get a negative number because as you're falling, you should be losing gravitational potential energy. Alright. So let's take a look at part b now.

In part b, we want to calculate the same variable. It's the change in the gravitational potential, but now we're going to choose our reference points, this arbitrary reference point to be somewhere else. So now what happens is we have the floor like this, we have the ball that's still 6 meters above the ground, but now what we're doing is we're sort of choosing this height here to actually be 0. This is where my y equals 0, and therefore, this is where my gravitational potential energy is going to equal 0. The ball is still going to fall 3 meters and so it's still going to end up at some height, but now we want to calculate the gravitational potential energy. Right? So what happens here, it falls to a height of y equals negative 3. So it's going to fall 3 meters, the Δy, the change is the same no matter how you set the numbers. So the change is still 3. And so we want to calculate the Δu. So now what happens is my Δu is going to be mg and then yfinal-yinitial. So what happens? We're just going to get 2 times 9.8 times negative 3, because what happens is we're going to get negative 3 minus 0. So that's our yinitial. So what happens here when you calculate this is you're going to get negative 58.8 joules again. So it turns out that in energy problems, whenever you're calculating the change in the gravitational potential, only the change in the heights is important. So you can choose your arbitrary reference point, your relative, you know, where y equals 0 to be wherever you want in the problem. That's actually not going to change what happens to your change in gravitational potential because it doesn't depend on the initial or the final height. What only matters is the difference between these two points right here. So the Δy was equal to negative 3 in both of the cases here, and so that's why we end up with the same negative of gravitational potential. So usually, one good rule of thumb is that if you know Δy, if you actually know the change in the height, you can set the ground level, right, where we set, you know, our ground level or our arbitrary reference point to be wherever you want, and that's where your ug is going to be equal to 0. Usually, what you want to do is you want to pick the lowest point of the problem because it's going to make your calculations a lot simpler. Alright. So that's it for this one guys. Let me know if you have any questions.