Learn about Projectile motion - part 6 Video

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Learn about Projectile motion - part 6

Learn about Projectile motion - part 6 Welcome back actually before I, I teach you how to figure out how high the ball went and you might already be able to figure it out. I want to show you a really kind a more intuitive way for figuring out how fast the ball went. I use the equation this first time just too really show you that this equation can be useful. But I personally always forget equations so it's—I find it very useful to kind of come with a common sense with of figuring it out as well. And really this equation was derived by coming up with the common sense with but I don’t know if that last statement has sense. But anyway let's move on. So let's say that same problem but let's just think about it without our equations. Because that’s always a good fall back when you're kind of you get a little bit of exam and you can't remember from the equation had a one half or two or minus or plus or t or t squared and so it's good just to think, think about what's happening. So when I throw up a ball straight up, you know I have a let's say it's baseball, it's a baseball. And I throw it straight up where you know my velocity, you know velocity initial is equal to well I threw it up with let's say that this is the variable. This is minus the velocity b sub y right? What's going to happened as soon as I throw it up, it's going to start decelerating, right, because I have the force of gravity. Decelerating it immediately, so gravity you know were saying minus 10 meters for a second, right. So this ball is going to keep decelerating, until it's velocity goes to zero, right. The ball if we were to, if we were to graph time and distance. Where this is time and then this is distance, right. At times zero were on the ground and the ball it's starts off going really fast and then starts slowing down and then it's velocity goes to zero and then it starts accelerating the negative directions, as going fast comes a fan and he’s on the ground again. So, what happens is that the ball starts fast starts going slower, slower, slower, slower, until it's velocity is zero and then it starts—and you can either call it, you could say reaccelerating in the opposite direction or decelerating really, but reaccelerating the opposite direction and then it hits the ground and actually we know, you know, not assuming nothing about air resistance etcetera, etcetera that the velocity that it hits the ground with is the same velocity, that it left your hand with just in the opposite direction. So there's a couple of interesting things here, the time at which its velocity is at zero. So that point right there, that’s going to be a t equals two, right. And we know that this shape is actually a problem, if you remember that from out of two why is that a problem, well what was the equation for, when we figured out the equation using that previous formula I don’t want to use it this time. But what was that previous formula it was change in distance, is equal to vi t plus at squared over two. So it's a problem but I think if you thought about it, you would realized also it's a problem right. And it points downward because a is negative so the t square turns negative so that’s why it points, it opens to the downward side. So I think that might make a little sense to you, so what we could figure out is if were given a t we could say well half of that number is let's say, let's say the t equals 10 seconds. T equals 10 seconds so we know that in 10 seconds the ball left my hand went up some distance and then came back down and hit the ground. What we also know then though is that t over two at five seconds the ball was essentially stationary for just moment. Its velocity, had― it decelerated, decelerated, decelerated, decelerated hit zero and then right before it starts reaccelerating again or reaccelerating downwards its velocity was zero at the time t equals zero. So what can we, what can we use that the fact that the ball decelerated from my initial velocity to zero and five seconds. What is that tell us? Well, we have the very simple equation, you know, change in velocity, change in velocity is equal to acceleration times time, right. That that’s you probably knew that before watching any of this videos and the change of the acceleration, well that’s just the final velocity minus the initial velocity it equal to the acceleration times time. In this situation what's the final velocity, remember were not going to go all the way here, were just figuring out from here to time equals two right, so what's the final velocity? Well were saying that point where the ball it's not going up and it's not going down, so its final velocity is zero, so zero minus initial velocity is equal to acceleration. Acceleration is the acceleration of gravity, minus 10 meters per second squared and then the time, the time is—if this is, you know, I know it's a little confusing because I'm using the t but let's say that this, this time is you know, I don’t know t sub zero, just to kind of make sure it's the sign of variable, it's actual time. So this is t sub not over two, right. Because the ball was motion less, right at the peak of it's, at the peak of it's—well were not on arc because we didn’t throw it in the—peak of travel. So it's acceleration times time but this time the time is going to be t upon over two, times t is not over two, right. So ones again we have, if we, let's see we can the zero doesn’t matter, we can multiply both sides times negative one and we get plus vi. And we get vi is equal to 10 divided by two, five meters per second squared t sub nine which was exactly what we got in the previous video when we used this formula. And I think makes sense to you that hopefully, this was kind of an intuitive way of thinking about what happened. And before I actually, I do the distance I actually want to graph what's happening because I think it just down on me that that might be something that’s will give you more intuition, I'm all about giving you intuitions and so you never forget this. Just as, so this is if we were to graph that’s ugly looking axis but I think you'll get the point. This is distance, this is time, we already said it's going to be like problem, that, right, where I'm now, this is t sub not over two, this is t sub not it launches really fast and then it slows down and then it is motionless right here and then it starts reaccelerating downwards. So if that’s the distance what is the velocity graph look like? Well the velocity graph I’ll draw it right below, I’ll draw it in another color just for a variety, all right, that’s a bold. So over, actually that’s not how I want to draw it, after I have, have to draw the negative side too, so this is time and then this axis is velocity. So actually we have the—so we start off at a positive velocity right? We started off at v sub i and what's going to happened here is the velocity decreases at a constant rate, right and that rate is just the rate of acceleration. The velocity decreases until at t sub not and let's see, at t sub not I'm going to switch back to yellow. At t sub not, t sub, oh whoops, I'm loosing around the tool it's actually look I was drawing something. The t sub not the velocity now is negative vi right. Remember, we said when the ball comes back down it is going at the same velocity just at the opposite direction. So at this point right here which is t sub not over two that corresponds to this point, right, which makes sense. Because that’s the point I wish the ball has no velocity and look the velocity is zero. So the balls starts going up really fast, slows down at a constant rate and what is the slope of this line, well the slope is just the acceleration, right because velocity is the acceleration times time. And then it's stationary for just a moment because its velocity is zero and then it starts accelerating or you could say decelerating or accelerating and the negative direction until the point that’s it's going at v sub I down. And of course if you were to graph acceleration, if I were to graph acceleration over time, acceleration is time, acceleration is constant its right here. Let me just draw it in the line. The acceleration is just a constant minus 10 meters per second so it's going to look like that and it's just the slope of this line. And if you know calculus, it will make sense to you that this line is the derivative of this line or this curve is like the derivative of this curve and even if you don’t know calculus I think it make sense to you that this is the slope of the this line. And just so if you haven’t learn calculus the derivative is just the figure away of featuring out a slope at any point along the curve so it's nothing too fancy. I’ll see you in the next presentation.

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Learn about Projectile motion - part 6

Welcome back actually before I, I teach you how to figure out how high the ball went and you might already be able to figure it out. I want to show you a really kind a more intuitive way for figuring out how fast the ball went. I use the equation this first time just too really show you that this equation can be useful. But I personally always forget equations so it's—I find it very useful to kind of come with a common sense with of figuring it out as well. And really this equation was derived by coming up with the common sense with but I don’t know if that last statement has sense. But anyway let's move on.

So let's say that same problem but let's just think about it without our equations. Because that’s always a good fall back when you're kind of you get a little bit of exam and you can't remember from the equation had a one half or two or minus or plus or t or t squared and so it's good just to think, think about what's happening. So when I throw up a ball straight up, you know I have a let's say it's baseball, it's a baseball. And I throw it straight up where you know my velocity, you know velocity initial is equal to well I threw it up with let's say that this is the variable. This is minus the velocity b sub y right? What's going to happened as soon as I throw it up, it's going to start decelerating, right, because I have the force of gravity. Decelerating it immediately, so gravity you know were saying minus 10 meters for a second, right.

So this ball is going to keep decelerating, until it's velocity goes to zero, right. The ball if we were to, if we were to graph time and distance. Where this is time and then this is distance, right. At times zero were on the ground and the ball it's starts off going really fast and then starts slowing down and then it's velocity goes to zero and then it starts accelerating the negative directions, as going fast comes a fan and he’s on the ground again.

So, what happens is that the ball starts fast starts going slower, slower, slower, slower, until it's velocity is zero and then it starts—and you can either call it, you could say reaccelerating in the opposite direction or decelerating really, but reaccelerating the opposite direction and then it hits the ground and actually we know, you know, not assuming nothing about air resistance etcetera, etcetera that the velocity that it hits the ground with is the same velocity, that it left your hand with just in the opposite direction.

So there's a couple of interesting things here, the time at which its velocity is at zero. So that point right there, that’s going to be a t equals two, right. And we know that this shape is actually a problem, if you remember that from out of two why is that a problem, well what was the equation for, when we figured out the equation using that previous formula I don’t want to use it this time. But what was that previous formula it was change in distance, is equal to vi t plus at squared over two.

So it's a problem but I think if you thought about it, you would realized also it's a problem right. And it points downward because a is negative so the t square turns negative so that’s why it points, it opens to the downward side. So I think that might make a little sense to you, so what we could figure out is if were given a t we could say well half of that number is let's say, let's say the t equals 10 seconds. T equals 10 seconds so we know that in 10 seconds the ball left my hand went up some distance and then came back down and hit the ground.

What we also know then though is that t over two at five seconds the ball was essentially stationary for just moment. Its velocity, had― it decelerated, decelerated, decelerated, decelerated hit zero and then right before it starts reaccelerating again or reaccelerating downwards its velocity was zero at the time t equals zero. So what can we, what can we use that the fact that the ball decelerated from my initial velocity to zero and five seconds. What is that tell us?

Well, we have the very simple equation, you know, change in velocity, change in velocity is equal to acceleration times time, right. That that’s you probably knew that before watching any of this videos and the change of the acceleration, well that’s just the final velocity minus the initial velocity it equal to the acceleration times time.

In this situation what's the final velocity, remember were not going to go all the way here, were just figuring out from here to time equals two right, so what's the final velocity? Well were saying that point where the ball it's not going up and it's not going down, so its final velocity is zero, so zero minus initial velocity is equal to acceleration.

Acceleration is the acceleration of gravity, minus 10 meters per second squared and then the time, the time is—if this is, you know, I know it's a little confusing because I'm using the t but let's say that this, this time is you know, I don’t know t sub zero, just to kind of make sure it's the sign of variable, it's actual time. So this is t sub not over two, right. Because the ball was motion less, right at the peak of it's, at the peak of it's—well were not on arc because we didn’t throw it in the—peak of travel.

So it's acceleration times time but this time the time is going to be t upon over two, times t is not over two, right. So ones again we have, if we, let's see we can the zero doesn’t matter, we can multiply both sides times negative one and we get plus vi. And we get vi is equal to 10 divided by two, five meters per second squared t sub nine which was exactly what we got in the previous video when we used this formula. And I think makes sense to you that hopefully, this was kind of an intuitive way of thinking about what happened. And before I actually, I do the distance I actually want to graph what's happening because I think it just down on me that that might be something that’s will give you more intuition, I'm all about giving you intuitions and so you never forget this.

Just as, so this is if we were to graph that’s ugly looking axis but I think you'll get the point. This is distance, this is time, we already said it's going to be like problem, that, right, where I'm now, this is t sub not over two, this is t sub not it launches really fast and then it slows down and then it is motionless right here and then it starts reaccelerating downwards. So if that’s the distance what is the velocity graph look like? Well the velocity graph I’ll draw it right below, I’ll draw it in another color just for a variety, all right, that’s a bold. So over, actually that’s not how I want to draw it, after I have, have to draw the negative side too, so this is time and then this axis is velocity.

So actually we have the—so we start off at a positive velocity right? We started off at v sub i and what's going to happened here is the velocity decreases at a constant rate, right and that rate is just the rate of acceleration. The velocity decreases until at t sub not and let's see, at t sub not I'm going to switch back to yellow. At t sub not, t sub, oh whoops, I'm loosing around the tool it's actually look I was drawing something. The t sub not the velocity now is negative vi right.

Remember, we said when the ball comes back down it is going at the same velocity just at the opposite direction. So at this point right here which is t sub not over two that corresponds to this point, right, which makes sense. Because that’s the point I wish the ball has no velocity and look the velocity is zero. So the balls starts going up really fast, slows down at a constant rate and what is the slope of this line, well the slope is just the acceleration, right because velocity is the acceleration times time.

And then it's stationary for just a moment because its velocity is zero and then it starts accelerating or you could say decelerating or accelerating and the negative direction until the point that’s it's going at v sub I down. And of course if you were to graph acceleration, if I were to graph acceleration over time, acceleration is time, acceleration is constant its right here. Let me just draw it in the line.

The acceleration is just a constant minus 10 meters per second so it's going to look like that and it's just the slope of this line. And if you know calculus, it will make sense to you that this line is the derivative of this line or this curve is like the derivative of this curve and even if you don’t know calculus I think it make sense to you that this is the slope of the this line. And just so if you haven’t learn calculus the derivative is just the figure away of featuring out a slope at any point along the curve so it's nothing too fancy. I’ll see you in the next presentation.

Transcription by: Scribe4you Transcription Services