Free fall 1 body - solved example

- [Instructor] Let's solve a couple of problems on falling things. Here's the first one, Deadpool drops from a height of 45 meters. Find the time it takes for him to reach the ground. G is 10 meters per second squared. So let's look at what's given to us. We have Deadpool, who's dropping from a height of 45 meters. So let's draw a diagram. Here's our Deadpool, a superhero who always puts his maximum efforts in catching bad guys. He's dropping from a height of 45 meters. That means the height right now is this height is 45 meters. We need to find the time it takes for him to reach the ground. So how do we solve this? Well, remember that whenever things are falling under gravity, they have a constant acceleration of 9.8 meters per second squared. In this problem, they've asked us to round it off to 10. So this is the acceleration with which Deadpool is gonna fall. Okay, so what? Well, whenever something has a constant acceleration then we can use three equations of motion to solve them, where V is the final velocity. U is the initial velocity, acceleration, time and S is displacement. Now, if you're not familiar with this equation, so you need a refresher, great idea to go back and watch videos on equations of motion, and then come back over here. And so we'll write down what's given to us and what is asked and we'll see which equation to use to solve the problem. Okay, it's given the Deadpool drops from a height of 45 meter, which means he's gonna fall down. He's gonna displace by 45 meters. So we know the displacement is 45 meters. We also know his acceleration, his acceleration is going to be 10 meters per second squared. Now what's important is accelerations can be both positive and negative, wherever objects speed up, this means the acceleration is positive. And whenever objects slow down, we say that exploration is negative. So in this example, notice Deadpool is gonna speed up as he falls, he's gonna go faster and faster, right? And so in our example, we'll take acceleration to be positive. What else has given? It seems like it's only these two things are given, right? But there's on one more information, which is pretty important. It's given the Deadpool drops from the height of 45 meters. Whenever something is dropped, we know it's initial velocity is zero, okay.? So we know the initial velocity of Deadpool, that is zero and we are calculate the time it takes for him to reach the ground that means we need to find what T is. So now we just have to select which of the equation we can use to solve the problem. And before I do that over here, great idea to pause video and see if you can choose, you can select which equation you would use to solve this problem. All right, let's go through each question one by one. Can we use the first one? No, because the first one has V in it, which we don't know. Can we use the second one? We know S we know U and we know, A. Hey, we can use the second equation. We can go for this equation. What about the third one? The third one doesn't even have T in it. So even third one we can't use. So we have a winner and we're going to use equation number two, and substitute and solve the problem. And again, if you didn't solve it earlier, now would be a great time to, again, pause and see if you can go ahead and plug in. Okay, let's go ahead and substitute. S is 45 meters that equals U, which is zero. And so this whole term goes to zero, which I will not write. Plus half times A which is 10 meters per second squared, times T squared. And now all we have to do is solve this equation and we'll be done. So let's simplify this. Let's see what we get. Two goes five times and our meter cancels over here. And the five goes nine times over here. So what do we have? We have nine on the left-hand side and we have T square on the right hand side divided by second squared. So if I multiply by second square on both sides, I will now get nine... Let me know that over here, I get nine second squared equals T squared. And now, since I want to calculate what T is, let's take the square root on both sides. Squared of nine is three, squared of second square is seconds equals T. And there's an answer, so T is three seconds. That means Deadpool takes three seconds to land on the ground. Now, before we proceed, one question we might have is squared of nine is both Plus three N minus three, right? So why did we ignore the minus three? Well, because if time is minus three, it is less than zero. And that represents the past because time is zero is the present it's right now. So, less than zero that present past, more than zero represents future. Since we are asked to calculate how long it takes for him to reach the ground after he has dropped, we care about the future. And it's for that reason, we only consider the positive time. And so you'll see most of the physics problems, whenever we're asked to calculate the time since we were asked about the future, we only consider the positive ones and we'll ignore the negative ones, so negative values. So anyways, let's now consider another problem. Spider-Man jumps straight up with the speed of 20 meters per second, calculate the maximum height he reaches. Again, given G is 10 meters per second square. Can you try to solve this one yourself? Again, make a quick drawing of this. See what is given what is asked and then pick an equation to use. All right, let's see. So we are given that the Spider-Man is jumping straight up, so let's draw that. So here's our Spider-Man, who's jumping straight up with the speed of 20 meters per second, we need to calculate the maximum height he reaches. So eventually he would reach a maximum height and then start falling back, right? So we need to calculate what that maximum height is. What is that distance? So again, let's write down what's given to us. We know that initial velocity with which Spider-Man jumps. So we know U that is 20 meters per second. We also know the acceleration. Whenever things are falling under gravity, immediately we know it's acceleration. Acceleration is going to be now this time, is it going to be plus or minus 10? Well, this time where as Spider-Man goes up, he slows down, right? He slows down as it is that he's losing velocity. And since he's losing velocity, the acceleration becomes negative. It's a deceleration right? So the acceleration becomes minus 10 meters per second squared. Again, that's the important part over here. What else is given? Again it feels like these are the only two things given, right? But something else is also given. Again, this is super important to figure out. We are asked to calculate the maximum height. And at the maximum height, we know the velocity of Spider-Man. At this point, if this is the maximum height, his velocity must be zero. That means we know his final velocity is zero. How do we know that? Why is it so? Well think about it, if Spider-Man did not have zero velocity, if say he was still going up with some velocity, then this wouldn't be the maximum height he's yet to reach the maximum height, isn't it? On the other hand of Spider-Man was going down with some velocity, tat means he has already reached some maximum height, and now he's coming downwards. So the only possible velocity for Spider-Man at the maximum height must be zero, right? Think about this. All right, and what we are asked. Well, we are asked to calculate that maximum height. So in this case, we're asked to calculate the displacement. That's what we need to know the displacement of Spider-Man. Again, which equation do we go for? Now, again, if you want to try this on your own, great idea to pause and see which equation you would go for, but let's see, we can't use the first equation because it does not have S, it is useless. What the second equation, hey, we can't use that because there's a T in it. And we don't know the time. So that only leaves us with the third equation. And so we can use equation number three. And if we substitute these values, which I'm pretty sure you can do now, we will get zero equals 20 meters per second squared, plus two times minus 10 meters per second square at times S and to save time, I'm pretty sure you can do this yourself. I'll tell you what the final answer turns out to be. If you calculate that, if you simplify, you will get the displacement as to be 20 meters. That means Spider-Man reaches a maximum height of 20 meters. And so whenever things are falling under gravity, because they have a constant acceleration, we can always use the three equations of motion and solve our problems. Now, there are a couple of things to be careful about though. One is the sign of the acceleration. When objects are thrown up, because their velocity will decrease, our acceleration will be negative. If the obliques are thrown down, the acceleration becomes positive. Another thing is sometimes the data is not given directly. It's a little hidden. For example, if we were given it reaches maximum height, but we had to understand that maximum height means the final velocity is zero. Similarly, in the previous problem, it was given that he drops from a height. We had to understand that drops means that initial velocity is zero.