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Current time:0:00Total duration:9:33

welcome let's continue doing projectile motion problems and this I think this video will be especially entertaining because I will teach you a game that you can play with a friend and it's called let's see how fast and how high I can throw this ball and you'd be surprised it's a it's actually a quite a stimulating game so let's let's let me just write down kind of the that let me write down everything we've learned so far change in distance that's might be too tight let me key stay with you I never use the blue change in distance is equal to average velocity times time and we know the change in velocity change in velocity is equal to acceleration times time we also know that average velocity is equal to the final velocity plus the initial velocity over two we know the change in velocity of course is equal to the final velocity minus the initial velocity this should hopefully be intuitive to you right it's just the how fast you're going at the end - how fast you're going at the beginning divided no no division it's just yeah I got I got stuck in a pattern it's just VF minus VI of course VF minus VI and then and and they might you probably already knew this before you even stumbled up on my videos but and the two non-intuitive ones that we've learned and they're really just derived from what I've just written up here if you ever forget them you could you should try to drive them and actually you should try to derive them even if you don't forget them so that you when you do forget it you can derive it but it's change in distance change in let me change it to lowercase D just to confuse you change in distance is equal to the initial velocity times time plus plus a T squared over 2 that's one of what I'll call the non-intuitive formulas and the other one is that the final velocity squared is equal to the initial velocity squared plus two ad and we've derived all of these and I encourage you to try to read arrive them but using these two formulas you can play my fun game how fast and how high did I throw this ball and all you need is your arm a ball a stopwatch and maybe some friends to to watch you throw the ball so how do we play this game we take a ball and we throw it as high as we can and we see how long does the ball stay in the air so what do we know we know the time we know the time for the ball to leave your hand what you essentially leave the ground and come back to the ground right so we are given we're given time what else do we know well we know acceleration right we know acceleration is just minus 10 meters per second if you're actually playing this game for you know for money or something you probably want to use a more accurate acceleration you could look it up on Wikipedia it's you know it's minus 9.8 one whatever whatever meters per second squared and and do we know the change in distance at first you're saying well Sal I don't know how high this this ball went but we're talking about the change in distance over the entire time right so it starts at the ground essentially the ground I'm assuming you're not like 100 feet tall you're essentially at the ground so it starts at the ground it ends at the ground so really the change in distance the change in distance Delta D is zero it starts at the ground and ends at the ground that's this isn't interesting this is a vector quantity right because the direction mattered if I told you how far to the ball travel well then you would have to look at its path and say how high did it go and how high waited to come back and actually if you want to be really exact the change in distance it would be the height from your hand when the ball left your hand to the ground so if you're like you know if you're like six feet tall or two meters tall the change in distance so that should be minus two meters but we're not going to do that because that that would just be too much but you could do it if you you know if there's ever a close call between you and a friend and you're betting for money so let's say you're given these things and we want to figure out so we want to figure out a couple of things we want to figure out well the first thing I want to figure out is how fast did I throw the ball because that's that's what's interesting because that is you know that would be a pure test of testosterone so how fast so I want to figure out VI VI equals question mark well which of these formulas can be used actually I'm going to do it first with the formulas and then I'm going to show you kind of an almost an easier way to do it where it's more intuitive but I want to show you that this these formulas can be used for four or fun with your friends so let's use let's see we know time we know acceleration we know the change in distance so we could just solve for VI right so let's do that so in this situation change in distance is zero let me change colors again just to just to change colors so change in distance is zero right change is just zero is equal to VI VI times time and let me put the G in for here so it's minus ten meters per second squared divided by two so it's minus five meters per second squared we could say almost so it's minus 5t squared right all I did is I took minus ten meters per second squared for a divided by two and that's how I got the minus five if you use 9.81 whatever this would be four point nine zero five something something anyway let's get back to the prom so if we wanted to fit solve this equation for VI what could we do well this is pretty interesting because there's we could factor a T out and and this actually and everything was cool about these physics equations is that everything we do actually has kind of a a real reasoning behind it in the real world so let me let me actually flip the sides and factor out a t just to make it confusing so I get T times VI minus five T is equal to zero right all I did is I factored out a T and I could do this I didn't have to use a quadratic equation or factor because there wasn't a constant term here so I have this expression and if I were to solve it assuming that you know VI is some positive number I know that there's two times where this equation is true right either T equals zero T equals zero or this or this term equal 0 v i- 5 t is equal to 0 or since I'm solving for velocity we know that VI is equal to VI is equal to 5 T interesting so what that what does this say there's 2 times if we knew the velocity we could solve it the other way we could say that T is equal to VI divided by 5 right these are the same thing just solving for a different variable but that's cool right because there are two times when the the change in distance is zero at time equals zero of course the change in distance is zero because I haven't thrown the ball yet and then at a later time or you know my initial velocity divided by five it'll also hit the ground again so those are the two times that the change in distance is here so that's pretty cool this isn't just math everything we're doing in math has kind of a application in the real world so we've we've solved our equation VI is equal to five T so if you and a friend go outside and throw a ball and it takes literally and you try to throw it straight up although we'll learn when we do the two-dimensional projectile motion that it actually doesn't matter really if you have a little bit of an angle on it because the vertical motion and the horizontal motions are actually independent or can be viewed as independent for each other but if you want to figure out and this velocity we're going to you're going to get if you play this game is going to be just the component of your velocity that goes straight up okay and I might be a little confusing and hopefully I'll make a little more sense in a couple of videos from now when I teach you vectors but the velocity if you if you were to throw this plot ball straight up and and time it you know when it hits the ground then this velocity would be literally the speed actually the velocity at which you throw the ball so what would it be let's see if if I throw a ball and it took two seconds if it took two seconds to to go up and hit the ground and I could use this formula and this is actually five meters per second squared meters per second squared on the x T right times T seconds so if it took two seconds so if T is two T is equal to two then my initial velocity is equal to ten meters per second and you can convert that to miles per hour we've we've actually done that in the in previous videos if if you throw a ball so fast it let's see if you throw a ball if you throw a ball that that that stays up in the air for I don't know for ten seconds for ten seconds then you threw it at 50 meters per second which is extremely extremely fast so hopefully I've taught you a little bit about a fun game in the next video I'll try to show you how to figure out how high did the ball go I'll see you soon