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Free fall - total time up & down solved example

Let's solve problems involving objects in free fall, and we are given/asked the total time to up and then come back down. Created by Mahesh Shenoy.

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  • aqualine ultimate style avatar for user jayden
    how dose spider man do that
    (2 votes)
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  • blobby green style avatar for user Himanshu Singh
    Suppose, we consider downward motion of spider man to solve first problem. In that case, can't we consider the final velocity to be zero as he lands in 8s and after landing, his velocity will come down to zero? Also, is there any difference between these two times : "lands in 8s" and "lands after 8s" ? Please give me clarity on these two doubts.
    (1 vote)
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Video transcript

- [Narrator] Well, let's solve a couple of problems of objects in free fall but when they're both going up and down, here's the first example. Spiderman jumps straight up and lands back in eight seconds calculate the velocity with which he jumped up given g is 10 meters per second square. So what's given to us, well, it's given that we have Spiderman so here's our Spiderman. It's given that he's gonna jump straight up like this goes up and then lands back and it takes him eight seconds for him to go up and come back down and we are asked to calculate the velocity with which he jumped up. So what velocity he jumps up, so how do we do this? Well, because objects in free-fall always have a constant acceleration this means we can go ahead and use the three equations of motion and solve what we want and we've solved problems like this in a previous video called free-fall one body soul example. But the difference over here is that Spiderman goes both up and comes back down and that total time is given to us. What's the problem over there? The problem is when Spider-Man is going up he's slowing down and during that time, his acceleration becomes negative because it's becoming slower and slower. On the other hand when Spiderman is coming back down his velocity increases he becomes faster and faster and during that time, the acceleration becomes positive. So we cannot consider the total motion because during one motion acceleration is negative and during the other motion the acceleration becomes positive which means we have to either consider the upward motion separately or the downward motion separately only then we can apply the equations of motion, right? So the first question we need to ask is which motion should we consider? The upward motion or the downward motion? Well, look at what is asked we are asked calculate the velocity with which he jumped up. So it makes sense to think about his upward motion, right? So that's the first thing so let's only consider the upward motion, upward motion which means we are going to consider Spiderman jumping all the way up like this and coming to rest at the top most point after that he comes back down. So we only consider from here to here so let's see what's given to us so in that we need to calculate what the initial velocity is. We know the final velocity, that is zero why is the final velocity zero? Because at the top most point he's at rest, isn't it? After that he starts coming back down he starts speeding up downwards, right? So we know it's final velocity zero we know the acceleration, acceleration is 10 but he's going up his velocity is decreasing so it's negative 10, but the big question is what is the time? Is it eight seconds? No, that's the time it takes for him to go up and come back down we want to calculate how much time it takes only to go up. So its gonna be less than that but how much? Well, here's the secret to solving this entire question you see, when Spiderman is going up his upward motion is going to be the exact reverse of his downward motion. He's going to be exactly the reverse of that you know why? Because while he's going up, he's losing velocity at 10 meter per second squared rate and when his falling down, he's gaining velocity at the same rate, since it's gaining at the same rate it's exactly the reverse, makes sense. This means the amount of distance he travels and the amount of time it takes for him to go up for him to go up, it's gonna be the same amount of time its gonna take him and the distance is gonna travel when he comes back down. Okay, does that make sense? Because the acceleration is the same that's the most important thing over here and as a result we can now say if it's gonna take the same time to go up and come back down that means it should take him half the time to go up and half of the total time to come back down. Since we know the total time is eight seconds half of that is going to be four. So that means he's gonna take four, let me write that down, okay he's gonna take four seconds to go up and four seconds to come back down. That's the secret that's the important part over here and now that we have this data we cannot just pick which equation we want to use. Go ahead and solve the problem so can you go ahead and try this yourself first pause the video and see if you can pick which equation. I mean, if we can figure out which equation to pick and see if we can solve for you. Well, let's see hopefully you've tried if you look at the first equation we know V we want to calculate U. We know A and we know TA we have everything we want and so we can pick equation number one. What about equation number two and three, just to check? Well, we can't use two because it has S in it we don't know S and we don't know U two unknowns we can't solve. Similarly, we can't use a third equation also because again we don't know U which we want and we don't know S also so two unknowns are there. So, we'll pick only the first equation because there's only one unknown and so if we substitute in the first equation V equals zero, U is what I want to calculate. Plus A is negative 10 meters per second squared and T is four seconds. So if we simplify, we get zero equals U minus because there's a minus sign, 10 times four is 40. So let me just put that 40 and let's see a second cansas over here. So we get meters per second, if we add 40 meters per second on both sides we will get 40 meters per second is going to be U and there's our answer. This means Spiderman jumped up with a velocity of 40 meters per second, let's do another one. Deadpool jumps up with 50 meters per second how long would it take him to land back? This is a very similar question so can you try and draw a diagram and see if you can solve this entire question yourself first go ahead, pause the video and give it a shot. Okay, hopefully you've tried so here's our diagram here's our Deadpool. It's given, he's gonna jump up with 50 meters per second, and we are asked to calculate how long it'll take him to go up and then come back down. Now, from what we saw in the previous video in reality, all we have to calculate is how long it'll take for him to come up or go up, right? Because the same amount of time will take him to come back down. So let's say if it takes him, I don't know, maybe 10 seconds to go up then we'll take 10 seconds to come back down and the total time would be 20 seconds. So that's all they have to do, just like before figured out how long it takes for him to go up. So we'll only consider the upward motion so let's go ahead and write what we know. We know the initial velocity is 50 meters per second we know it's acceleration because he's going up, he's slowing down. So his velocity will decrease and so his acceleration is going to be negative 10 meters per second squared. Time is what we need to calculate and we have his final velocity, his final velocity is zero and just like before, if you look at the three equations check which equation to go for, we have to go for the first equation, because again the other two equations have S in it and we don't know S and we don't know U so these equations have two unknowns. So let's pick the first division and we will solve it and so if we subsidize now in this first equation the values, I mean, which, I'm pretty sure you can do all by yourself just to save time then the time turns out to be five seconds. So, if you had not solved this before again, great idea to pause and see if you're gonna get this answer. So is the answer five seconds? No, this means Deadpool takes five seconds to go up and because we saw the upward motion is exact reverse of downward motion, is gonna take the same time to come back down. That means five seconds to go up 4 five seconds to come back down that means the total time taken that's I asked, how long did it take for him to land back total time, that's our final answer. Total time will be 10 seconds double of this five plus five. So it's going to be 10 seconds and this is our answer this is only for the upward motion. Okay, so what do we see in this video? Well, we saw whenever we have problems which have both upward and downward motion we can choose only one of them to solve our problem and the secret is the upward motion is exactly reverse of downward motion. This means that they're gonna take the same time to go up and come back down.