Hi everyone. In this video, I'm going to be talking about the difference between distance and displacement. And I'll do a practice problem, specifically one that uses the Pythagorean theorem, or in other words the formula a squared plus b squared equals c squared. So, the problem that we're going to be looking at today says "A student walks his dog to the park. He starts at point P and walks 200 meters due north and then 350 meters due east. The entire trip takes him 400 seconds." And the question that I'm going to be answering is: "Calculate the student's displacement, showing your work. Then, draw and label the displacement on the diagram." Um, before we get started, let's review our definitions of distance and displacement. So, distance is shown in this diagram in purple and it's the length of the path taken between two points. Displacement is shown in green and that is the shortest distance between the initial and final positions. I like to think of displacement as the shortcut. So, if we look at the question, the easiest thing to start with is just finding the distance. Even though they didn't directly ask me for that, we might need it later. Um, the purple arrows that I have highlighted show the distance because that's the path that was taken. I would simply just add up those two numbers: 200 meters plus 350 meters gives me 550 meters, and that's my distance. Um, but we're supposed to look for displacement, which I have highlighted in the green dotted line. The important thing to see here is that this is a right triangle. And that means we can use the Pythagorean Theorem, um, the formula: a squared plus b squared equals c squared. I have a, b, and c labeled on my diagram. I have "a" labeled as the 200 meter side and b labeled as the 350 meter side. Those two are interchangeable; that doesn't matter. What matters is that c is always the hypotenuse, or the longest side of the triangle. And in physics class, we're now calling that the displacement for a problem like this. So I'm going to go ahead and plug in my numbers: 200 squared plus 350 squared equals c squared. This next step is optional to write down because you can plug this whole thing into your calculator at once, but some people like to type in 200 squared and see that it's forty thousand. And then 350 squared and see that it becomes 122,500. We would add up those two numbers and get 162,500 equals c squared. Um, I don't actually want c squared though I want c by itself. So that's why I'm going to take the square root of both sides. When I plug that into my calculator, I see that the square root of 162,500 is 403. Um, it has a decimal after it but I just wrote down 403 and I wanted to put meters because I know that if a and b are measured in meters, c will also be measured in meters. And that is my answer: displacement is 403 meters. To really complete this diagram, I want to make sure I actually write down 403 meters next to that dotted line that I drew, and it's important to also draw an arrow head showing that the person started at point A and this is their end point. The arrowhead makes sure that you don't think they started over here and ended here. So this is how I would answer that question, um, what is the student's displacement, and to draw and label it on the diagram.