 Hi, my name is Brad Langdell. I want to talk to you about the applications of the acceleration due to gravity. The big G, actually the little G, but it's big because there's so many things you can do with it. These questions come from the section of notes called Applications of acceleration due to gravity off the website. Check them out. Here are the solutions. A couple of things keep in mind Acceleration due to gravity. It's a vector that means it can have a positive or negative value. In this case It always has a negative value. Important to remember your problems won't work out unless you include that. The acceleration due to gravity can be used in place of acceleration in any kinematics formula. As long as the object is falling near the Earth's gravitational field, it works. It's actually not 9.81 meters per second absolutely everywhere, just at sea level. More on that later on if you're interested, check the website. And it's an exact value, which means it doesn't count for sig-digs. You don't worry about this for sig-digs or anything that comes off your formula sheet. Here are some examples. Classic. An apple is dropped from a height of 1.25 meters. How long does it take the apple to hit the ground? Here's a picture. Here's an apple. It's falling through a distance of 1.25 meters. Now the only other piece of information we're going to need is that the initial velocity of this apple because it's being dropped is 0 meters per second. Okay, that's really important. A drop means initial velocity of 0 meters per second. And of course, we're going to need to know our acceleration due to gravity negative 9.81. meters per second squared. And hey, did you notice how I drew this as a downwards arrow for that displacement? That displacement is also negative because the apple is falling downwards. That negative sign will be important. All right, what do we got for formula here? Well, I need d, I need vi, I'm looking for time. How long does it take? So I think I'm going to use displacement is vi-t plus 1.5 at squared. Now the great thing about this formula is check it out. Initial velocity is 0. So no matter what the time is, I don't even care what the time is at this point. If I times it by 0, it's going to cancel out. I don't even have to write that term. It's nice. All right, I can substitute in for my other values. Don't forget your negative sign. There we go. And I can do a little bit of algebra now. So on the calculator I'm going to throw in here negative 1.25 meters. I'm going to times it by 2. That's going to get rid of the 1.5. I'm going to divide it by negative 9.81 meters per second squared. Gets rid of that negative 9.81. And I don't really know why I put 1.25 meters in there again. But I can fix that. That's going to be t squared. So when I divide by this, I'll have t squared all by itself. t squared is about 0.25. Second squared would be the units at that point. But I don't want second squared, nor do I want t squared. So the last step of my algebra, I got a square root here. So my time to three significant digits is Come on board. 0.505 seconds. There we go. If you want to know how long it takes something to hit the ground from being dropped, initial velocity of zero, all it depends on is the displacement. There you got it. Hey, now how fast is that apple going when it hits the ground, I wonder. Let's figure it out. We're looking for a final velocity here. And I already know my initial velocity, and I already know my time. And you know, I got the acceleration. I got the displacement. You could use a lot of formulas here. But I'm going to use this one because I think it's going to be easiest, what we call the no time formula in my classroom. Final velocity squared is the initial velocity. Hey, that's zero. So that cancels out. Don't have to even write that in. Times equals two times the acceleration. Negative 9.81 meters per second squared times our displacement, which we already know is negative 1.25 meters. Okay, I'm going to type this into my calculator. Let's evaluate that right hand side. Two times negative 9.81 times negative 1.25. And see what that results. Okay, 24.5. But I want to square root that to get what the final velocity is. So it looks like it's going to go at about 4.95 meters per second for our final velocity. Two, three significant digits. So there you go. That's how fast that apple is going after it has been released from a height of 1.25 meters. All right, I got another one here to show you and then you can take a look at some other videos. How high does an object go if you throw it in the air? So we got a pizza pie here. This pizza pie is being thrown up in the air with an initial velocity of 5.2 meters per second. Initial velocity. I want to know how high is this thing going to go up in the air? Now here's a cool thing about things that go up in the air. They stop eventually. And when they stop they have a final velocity of zero. And we're going to call the final velocity zero here because we're only interested in this movement from ground level up to some displacement. That's what we want to find. The question can stop there so I can stop final at zero meters per second. Now the other piece of information of course I know here is the acceleration due to gravity negative 9.1 meters per second squared. So I'm thinking now what's a formula that has initial and final velocity that has everything I need and nothing I don't? It's that same no time formula we were looking at a minute ago. The final velocity in this case is going to be zero. My initial was 5.2 meters per second. And I'm going to square that whole number times two by the way pizza boy plus times negative 9.81 meters per second squared times D and that's what I'm looking for. So I'm going to go and do a little evaluating here now. 5.2 squared is going to give me 27.04. Now technically the units there are meters squared per second squared plus two times negative 9.81 negative 19.62. Technically the units there are meters per second squared times displacement. So what do I got to do here to get that D by itself? I still got a zero on the left. Well I'm going to subtract 27.04 from both sides negative 27.04 meters squared per second squared equals negative 19.62 meters per second squared times D. And now we'll just divide to get rid of that negative 19.62. Put in negative 27.04. There we go. Divide it by negative 19. Let's do this. Divide it by the answer. And so this is going to go one point. How many sig digs we got? Two sig digs. 1.4 meters in the air. Classic question. How high does it go? All right so there's two problems. If you're looking for more I'm going to make another video part two that has more problems from this section answered. So check it out at the website ldindustries.ca