# tv Earth Focus LINKTV August 28, 2014 6:00pm-6:31pm PDT

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*little*rule that'll tell you exactly which way and how fast it goes. and the

*little*rule is this. take your two vectors, one representing ground speed or the speed through the air, and the other representing the speed of the wind, and make those into a parallelogram. since they are right angles here, that parallelogram's gonna be, in this case, a square, because the sides are equal. make a square. and then what you do is you join from here to the diagonal, and you make a vector like that. and guess what, gang? guess what? that's the direction that the aircraft will travel. and, furthermore, it tells you how fast it's gonna travel. because if this is 100, and this is 100, and that's a 45 degree angle, and it would be for both 100, yeah? it turns out, so this will be-- this will be the square root of 2 times 100, something like 140.

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*little*rectangle, yeah? you see how now this is a rectangle? and what's the diagonal of that rectangle represent, gang? - the direction. - that's right. now, you'll be blown off course only that much. and you know what, if you had a ruler

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*ball*and i roll it across the table, okay? as it rolls across, let's suppose i took strobe pictures: one here, one here, one here, one here, equally spaced times. you know what? i'd find equal space times would get equal spaces of distance. do you know why? because the

*ball*is rolling at constant velocity. i mean, it's rolling here, then here, then here, then here. so my

*little*velocity vector would simply be like this.

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*little*push to get it going. but once i get it going, i let go. it kind of rolls over on its own, and it rolls steady, steady, steady, steady, okay? and so these

*little*vectors would just show me that it's rolling at constant velocity. let's suppose, instead, i take it and i drop it. [descending whistle] oh, what's it gonna be now? here is it up here, see, then i drop it and it goes to here, and to here, and to here, and maybe down in here. now up here, no velocity. but over here, a

*little*bit. and over here, a

*little*bit more. and you know the velocity is increasing, because it's accelerating. and we've talked about acceleration. and when the acceleration is due to gravity, we just call it g, remember that? and we know that g for the planet earth is-- check your neighbor. what's the numerical value of g for the planet earth?

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*little*bigger here. it's faster here than here. and over here, i'll make it like this even more. and that's because the speed, the speed picks up according to the acceleration and time. and the longer the time, the faster you're going, but you know that anyway. and so this is the relationship we've talked about last time. how fast something goes depends upon how much it's accelerating and how long a time it's doing that, isn't that true? let's do a review. if i took this thing and held it up in the air and let it go. [descending whistle] at the end of one second, what would its speed be? 10 meters per second, see?

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*ball*just fell by the window at 50 meters per second. someone would say, "how did you know that?" well, i just know that. one second later, boom, hits the ground. okay, how fast was it going when it hit? you couldn't see it then. check and see if you're sitting next to somebody who know the answer to a question like that. how many say 60 meters per second, show a hands? hey, my people, all right, all right, that's right. because every second go by is gonna pick up 10 meters per second more than it had before, we're learning the stuff, huh?

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*ball*up in the air and then having it drop.

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*little*bit. but, anyway, that's what we're gonna do here. does that answer your question then? so that's the speed we're gonna pick up. now, i'm gonna get to the part that's a

*little*difficult for some people. that's how fast it goes. how far is it gonna fall? oh, we'll get it all get mixed up. how fast, how far? how far is different than how fast, right? and how about it, gang, when i drop this thing? [descending whistle] it's gonna pick up distance, yeah? you see it getting further, further apart, huh? what is the rule for how far it falls? is there a rule? how many would say? no, there's probably no rule for that, it's different every time. come on, gang, what's the rule? do you remember? yeah, it was distance falling, d for distance, equals, average out the g, g squared. and if g is gonna be 10, and it will be for the planet earth, then a half of 10 is 5, so we could just say, 5t squared.

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*ball*, i get up on top of a cliff and i drop it. [descending whistle] how far down is it underneath one second later? check the neighbor. how many say begins with an f, ends with a ive? [laughter] yes, five meters, five meters down, okay? remember that any object that falls from rest will fall a vertical distance of five meters in the first second of fall. if two seconds goes by, how far will it have fallen then? even more. how much total and how would you find it for two seconds, gang?

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*little*rule right here. if two seconds goes by, you take 2 times 2 is 4 times 5, 20 meters. it would have fallen 20 meters. and let's suppose 10 seconds went by, you're in the airplane. you're dropping from the airplane. it takes 10 seconds to hit the ground. so if you're sitting next to someone who knows how fast-- i mean, not how fast, how far down the ground is? well, 10 plus 10 plus 10 plus 10 plus 10 plus 10 plus 10 plus 10 plus 10 or what? it's 100, honey, 100, okay? so now you got 100 times-- it's gonna be 500 meters down. so if you're ever falling off a cliff and it takes 10 seconds to hit the ground, your last thought will be, "hey, it took-- i bet you i fell 500 meters." that's how far you'd go. and you see that. any questions on all this? so we're really summarizing what we talked about last time. there's a difference between how much you pick up speed, okay,

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*ball*when it rolls off the table?

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*ball*, the

*ball*is rolling at constant velocity. i got it going somehow, but once it's rolling, it's rolling. and let's suppose there's no gravity at all, none. and what's gonna happen? the

*ball*is gonna just keep rolling like that. and if i have an arrow representing the speed at every time, it might be something like this.

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*ball*is rolling along and now i push it. when i push it, it gains speed. but if i don't push it, it will just keep rolling steady, steady, steady with no change. and, furthermore, there's nothing this way obstructing it. now, there is some air drag, but very, very

*little*compared to the tendency of that

*ball*to just keep crashing through. so the

*ball*goes steady, steady, steady. and rolling off the tabletop, if there's no gravity, would continue steady, steady, steady. but it doesn't continue like that, because there is gravity.

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*ball*we just hear it dropping, if i let it go, it falls here maybe. then falls in here, then falls in here, and then maybe fall down to here, okay? and then i'll have like a

*little*speed like this, a

*little*more like this and a

*little*more like that, and down here even more. what happens, as the

*ball*is traveling like this, it does this. it falls. so when it gets out to here, it really doesn't. it never does get out to there. it falls underneath, guess how far underneath it falls, one guess? all right, two guesses. [laughs] it's gonna fall right to here. and instead of getting out to here, gravity would have pulled it down to guess how far? it will exactly match what's happening over here. kind of neat, huh? it will fall to here. and then instead of getting out to here, and no table to support it, it will fall underneath.

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*ball*really is-- that's not drawn very well now. it should be a

*little*more-- like that. and, hence, the

*ball*curves. but the neat thing is that what happens sideways doesn't change. it's only the downward part that changes. and you know why that's true? the gravity pulls which way again? beginning with a d, ends with a "own." - try it. - down. down, gravity pulls down. and so guess which way it accelerates? - down. - down. how about accelerating sideways? no. so the sideways part stays the same. [mwah] isn't that nice?

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*ball*and you throw it up in the air like that, okay? here's the speed like this, the speed gets less, less, less, now it's about to pick up. all along here, the sideways part stays the same. the sideways part doesn't change, only the vertical part does. and that's kind of neat. and human beings didn't know that for a long, long time. the sideways part doesn't change. question? and one thing that might have, maybe occurred without figuring it out, is the question of how long does it have one of those speeds drawn in there? how--what kind--how long does it have that speed? are any of those an average speed? yeah. well, no, this would be the speed at any instant, lee. now, in the absence of air drag. it turns out with a projectile-- usually there is a lot of air drag like with a cannonball.

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*ball*that rolls off the table, takes the same time to hit, as one that drops. do you believe that? remember the first day we talked about the rifle? you take the rifle and you fire it, and you let go of the bullet. and one bullet falls down, and the other goes out, which one hits the ground first? we talked about this. which one does hit the ground first, gang? take a guess. i'll give you a hint, ss. same same. you not be knowing that? let's try it. and i'll come back to this swimming pool thing in a minute. there's a

*little*device here that will shoot a projectile,

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*little*spring, a

*little*spring here. i'm gonna compress the spring. and when i do that, i can put a projectile here, and watch this, gang, a

*little*spring gun, okay? out it goes, no surprise. but i've got another

*ball*that i can put on the end here like this, and when i go like this, it falls essentially straight down, a

*little*bit out, okay, but kind of downish. this one goes outish. now, i'm gonna do them both at the same time. when i do them both at the same time, you guys got to figure out, hey, which one is gonna hit the ground first, the one that just drops down, or the one that... [whistles] ...goes out? a lot of people think, "oh, the one that's fired out is gonna be in the air for a longer time." do you know why? because gravity gonna start to pull it. "oh, i didn't know you're moving, go ahead." and gravity not gonna pull so hard. what do you guys think? let's try it.

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*ball*, throw another

*ball*out, same time. since you have that--with things just dropping straight down, it goes 10 meters per second. but if it also is going horizontally, doesn't that object have to go-- be going-- traveling at a faster speed than the one that's just dropping vertical? if you're gonna get an angle that's more of this way, yeah. see what happens in freefall though that the vertical speed will keep increasing, increasing, increasing and become very, very big compared to that horizontal speed you have. so it looks like you're going straight down. what do they do in the old cartoons where the roadrunner runs off the cliff, you know? the roadrunner runs like this: da-da-da-da-da-da-da, aaaaah! foooom! okay? they go straight down. but that's a

*little*bit different than in that, gang,

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*little*angle. and that angle gets steeper and steeper as time goes by. but here's the point i want to make, gang. if it takes four seconds to go from here to here, it takes four seconds to go from here to here. so i ask people when they get up there, do you suppose if you jump, you could hit the pool? and how would you find out? and here's what you do. you figure out how fast, how far out you could jump in one second, okay, in one second, then multiply that four times and you got it. it turns out you'll really hit way down here. let me--i hit something like way in here, see? in one second, i can jump that far, two seconds that far, three seconds that far, four seconds that far. so it turns out, it gets very, very steep very, very quickly and you get so far. knowledge of physics.

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*little*further upstream, okay? you're sitting down, they put out the big tablecloth, the kentucky fried chicken, the kool-aid, the mcdonald's, the burger kings, whatever. all of them right out there, right? you ain't checking out the food. what are you checking out? potential friend again. and son of a gun, there's an even more delightful person, okay, bam, bam, bam, bam.