 Hello everybody, I'm going to help you out here working through some falling object calculations. There's a little bit of theory we're going to start off with. The first thing we've got to think about is the fact that when an object falls, any object, doesn't matter how heavy it is or what size it is, if there's no air resistance acting on that object, it's going to fall with an acceleration of negative 9.81 meters per second squared. That's the acceleration due to gravity. That number is in your data booklet, so you don't have to memorize it, you can look it up when you need it. The other thing you need to keep in mind is that all this number is, is an acceleration. So you can just replace the A variable, the acceleration variable, in any of our kinematics formulas with this number and then do the calculation as you normally would. And we have a new kinematics formula we're going to be looking at here today that we're going to get a little bit of practice with, with this topic. So let's try a couple of these out. Here's the first one. So I'm dropping a rock on some size 20 students, getting them to work a little bit harder. I drop the rock from rest and it takes 3.5 seconds to hit the ground. How high was the rock dropped from? Now there's a couple of things here we have to kind of start off thinking about. First of all, that phrase drops the rock, or drops the rock from rest is really important. You see when you drop an object, like the diagram is showing here, the initial velocity of that object, how fast it's going when you first let go of it, is 0 meters per second. That's what it means to drop an object, is you let go of it, that moment you let go of it at the very initial part of the movement, it's not moving. So you have to remember when you see a question like this, that when you see the word drops, you have to think that means vi equals 0. And that's a little tricky at first, but as you practice more of those problems, you'll start to remember it. So that's the first variable I have in this question. The next variable I have is the time, says it takes 3.5 seconds to drop. So I'm going to make a little variables list over here. I have initial velocity of 0 meters per second because it was dropped. I have a time of 3.5 seconds. They want to know how high was the rock dropped from. So that variable, how high something was dropped from, is displacement. And that's what I'm going to solve for. And the other variable we have here is the acceleration. Now I know it doesn't say what the acceleration is. When an object falls, it has an acceleration of negative 9.81 meters per second squared. We do have to have that negative sign in there. Let's try out a formula. So the formula we're using here on your datasheet is d equals vi t plus 1 half at squared. And it probably seems more complicated than it really is. So let's try and substitute into it, see what we get. In place of vi, I'm going to put 0 meters per second. Time was 3.5 seconds plus 1 half multiplied by the acceleration. That's negative 9.81 meters per second squared multiplied by the time. So that was 3.5 seconds. And there's a squared on that time. So we're going to make sure that we type that into our calculator. Now 0 times 3.5, that's just going to be 0. So you don't even have to worry about typing that into your calculator if you don't want to. You could just type in the 1 half times negative 9.81 times 3.5 squared. And make sure you only square the 3.5 when you do that. So when I type that through my calculator, I end up getting negative 60 meters. You might be wondering, why do you get a negative number in there? That seems kind of weird. Well, there's a good reason for that. This rock, or whatever object it is, fell downwards. And since displacement is a vector, and it has magnitude and direction, the negative is what the math is doing to tell us that the object will fall down. So it's important to remember that if you have any objects which are going to fall downwards, they should have negative displacements. And we're going to use that idea in the next question. All right, so here's another one we're going to try out. It's another object that's being dropped. So I've already written in here that that means the initial velocity is 0 meters per second. Remember, anytime an object is dropped, it means it starts off from rest at 0 meters per second. And then it gives us how far up in the air it started. So that means the displacement here is going to be, again, negative 150 meters. Why negative? Because that cannonball is going to fall downwards through 150 meters. This is a really, really long drop, I guess, for this cannonball. How long does it take to hit the ground? So I'm going to see if I can find time. And the acceleration is the acceleration due to gravity again, negative 9.81 meters per second squared. I'm going to use the same formula I used in the last problem, d equals vi t plus 1 half at squared. And that forming those on your data sheet, so you don't need to memorize it. But I'm going to use it a little differently. Now I'm going to put in for displacement negative 150 meters. The initial velocity was 0 multiplied by the time. And I don't know what the time is, but that's OK. I'll just put in a t plus 1 half negative 9.81 meters per second squared times the time, which I don't know squared. Now when I start to go through and do my algebra here, the first thing I want you to notice is that 0 multiplied by t. Well, I don't know what t is, but I know that any number multiplied by 0 is 0. So that term just sort of cancels out. And here's what I have left over once I sort of in my brain cancel that term out. And I'll drop the units to make it a little easier to see. Negative 150 equals 1 half times negative 9.81 times t squared. So the next thing I would probably do here is I would multiply together the 1 half and the negative 9.81. So I'm just typing in 0.5 times negative 9.81. And I'll rewrite out what I get. So that's negative 4.905 times t squared. I want to get that t squared by itself. So I'm going to divide by negative 4.905. There we go. So 150 divided by negative 150 divided by negative 4.905 is going to work out to about 30.5 h. Now that's equal to t squared. So to get that t by itself, we're going to square root both sides. And the square rooting will cancel out the power of 2. And will give us an answer of 5.53 seconds. Now, of course, if you're not sure if that's right or not, if you want to check your work, all you have to do is take that in time and substitute it back into your original equation up here. And if you can verify it, if it'll work out to 150 meters, then you know you've done it correctly. All right, now we're going to try one more. This one's pretty tricky in terms of the algebra, but I'm very confident you'll be able to do it with a little bit of practice. So we have another object. Now it's an egg, and it's thrown out of a window. It doesn't say this dropped, though. It says it's thrown downwards out of the window. So I don't know if this means the initial velocity is going to be 0 or not. Gives us the high above the ground the window is. So this egg is going to drop negative 11.2 meters. It takes the egg 0.550 seconds to hit the ground. And I want to find the initial velocity now. So we're going to solve for that other variable in the equation that we haven't solved for yet. And like all these other problems, today the acceleration will be the acceleration due to gravity. All right, well, you know, not too different. We're going to use the same formulas before. And I'm going to substitute into it like I did before as well. We want to put those units in when I do my initial substitution. It's OK if you drop them after that. This kind of helps you recall if you need to do a unit conversion or anything like that. 0.550 seconds squared. All right, now what I'm going to do here is just a little bit of simplification. So nothing to simplify on the left-hand side of the equation. That looks fine. Maybe I'll just write this as 0.55vi. Since that's the way you usually see it in math class, the number first and the variable second. Then in my calculator, what I'm going to do is I'm going to go and multiply together all of this. I'm going to work out what this works out to. So in my calculator, I'm typing in 1 half. Or if you want to write 0.5, that's fine too. Times negative 9.81 multiplied by 0.550 squared. Now that gives me negative 1.38 to round it off. And that is what I'm going to now move over to the other side of my equation. So I've sort of done all my simplifying. Now I'm going to go through and do a little bit of algebra. So I'm going to add to both sides 1.4838, 1.4838. OK, let's see what we get. So that gives me negative 9.7162. And that equals 0.55 times the unknown variable vi. One more step and we're done. I'm going to divide both sides by negative 0.55 and see what we end up with. And I end up getting from my initial velocity a negative number, negative 17.7 meters per second. And I think that makes pretty good sense that it should work out to a negative number since I know that this egg was thrown downwards. I hope this video helps you work out some of these falling objects problems. You're going to see a few more questions like this on your UniB review assignment.