[laughter] and you count off the seconds, you say, "according to my calculation, we're several kilometers high." what's this delightful person say to you? "you schmuck, i'm not gonna go home with you, okay?" you--"you don't have to do that." how could you do that? how could you impress that delightful person? there's a way to do it. okay, we haven't talked about torques yet. but if you knew about torques, you could do it. let me show you what to do. what to do is you don't drop the rock like that. you get your board, long plank. then you roll a great big piece of rock on it like that. that's counterbalance, all right? then what you do is you crawl out to the edge of the board, okay? [laughter] and you get out on the edge like that, okay? and you take your rock and you drop it. "one, two, three, four, five. "5 times 5, 25, 25 times 5, 125.

we're 125 meters high." what does the delightful person do over here? the delightful person says, "oh, wow." knocks the rock over and guess what happens, huh? so the rock comes down, here you go, you're in the water. you come up and say, "fortunately, i can swim." what comes down back after you. you don't have to do it that way, gang. there's another way. anyone know? lee? just throw the rock. throw the rock up in the air, right? throw it horizontally. how about you throw it up in the air, who's gonna be lonesome? how about you take the rock and you throw it down and you start counting, who's gonna be lonesome, right? if you want to avoid lonesomeness, which way do you throw the rock in, huh? you throw it straight out. ain't that right? you throw it straight out. [whistles] now the time it takes to hit is gonna be the same time to hit as if you dropped it. you see that? so it works out neat, doesn't it? i've done this before, i've been on a cliff. you want to know how high it is? throw it straight and count the seconds off.

it's the same as if you dropped it. it works. it's nice. you know why it's nice? begins with an f, it's physics, good physics, yeah, yeah. would you like to see what, like, a tough question would look like that has to do with everything we're talking about right now? how many say, not particularly. let me show you what a tough type question is that invokes all the ideas we've been talking about. let me show you. a baseball pitcher at the top of the tower throws a rock, throws a rock straight out. and it turns out the tower is five meters tall.

and it turns out the rock thrown as fast as the baseball pitcher can throw it goes 25 meters downrange. your question is this, and usually i would give you a weekend to think about it. what is the speed of the ball to do such a thing? think. hint, we're throwing it sideways now. hint, the speed of anything is the distance it goes divided by the time it takes. without yelling out the answer, is there anyone that has an answer? 1, 2, 3, 4, 5, 6, 7, 8, let's get two more, 9, 10. 10 people have an answer, 40 people have no answer, not yet.

let's let the equation guide our thinking, gang. how fast is distance over time? the pitcher is throwing the ball horizontally. are we given the horizontal distance that the ball goes? yes, we are. and that distance is what? twenty five meters. are we given the time that the ball is in the air? no. therefore, the problem can't be done. boom, impossible. wait a minute, we're not given the time but we be knowing enough physics to figure out what the time is. see how many of us can figure out how long is that ball in the air. let me make it easy, let's suppose the dude just took the ball and drop it. how long would it be in the air, beginning with a w.

- one. - one. but now he ain't dropping it. he's throwing it sideways. check the person sitting next to you and see if the person sitting next to you is any resource in this problem. how many say it's one second? show our hands. that's right, it's one second, gang. 'cause if it's gonna take one second for something to fall five meters and you toss it out, it's still five meters vertical. it's like this thing over here. if this is five units down, this one comes out, it's still five units down stretched out, huh? so it's gonna take one second. so 25 meters divided by 1 second gives you 25 meters per second. isn't that neat? there's some good physics there, gang. do you like? let me ask you a question. would the ball be in the air for a longer time if there were a hill like this?

yes. would the ball be in the air for a longer time if the earth's curvature came into play? yeah. it turns out if he throws that thing really fast, it might go so far out that the curve of the earth is falling away. you see that? in fact, if he keeps throwing faster and faster and faster, he might throw it off the earth altogether. isaac newton, physics type in 1700, figured it out like this. consider a mountain on the earth that's so high that it's up above air drag and put a cannon up there. now we're up above the drag of the air. if you fire the cannonball and there was no gravity, none, the cannonball would... [descending whistle] go in a straight line.

but the cannonball doesn't go in a straight line. you know why? because there is gravity and gravity pulls it down. so what cannonball does... fooom! it maybe falls like that. do you know what would happen if i fired it faster? fooom! it would be up for a longer time but still fall, wouldn't it? let's suppose i fire it even faster, longer to hit or same time to hit or less time to hit? - longer. - longer to hit. fooom! you know what i'm gonna do now, gang? i'm gonna put all the powder in, all the powder. i'm gonna fire that thing really fast. watch this. fooom! is the cannonball falling? is it still falling? yeah. fooom! so you got to move the cannon out of the way. isaac newton realized

that if you fired a cannonball fast enough, it would fall all the way around the world, around and around and around. that speed is high, very, very high. but that's how we put things into orbit. we simply put-- instead of using a cannon, we put things on a rocket and piggyback it up and get up there and then we get up there, they fire it out and something falls around and around. next time you see the space shuttle on tv, you see the people inside them, you see the views of the earth, and realize that space shuttle is falling around and around the earth. it's going so fast sideways, by the time it falls a little bit, the earth is curved the same. isaac newton was able to calculate how fast the cannonball would have to go. isaac newton was a genius. you know, there are people on this campus

that can calculate how fast the cannonball would have to go. and you know what? there are people in this room who could calculate with no pencil, no paper, only their minds how fast the cannonball would have to go. and i think that 80% of the people in this room can make that calculation if i guide your thinking. can we try it? you want to see who you are? let's try. let me give you a geometrical fact. we live in a world that's curved. we know it's curved because if you put a laser one meter off the ground and you fired the laser beam out over the desert like the mojave desert in california, perfectly flat for miles and miles and miles. if you fired that laser beam, you'd find out the laser beam over here, it looks like to people it's pointing up. but it's not pointing up here. it's just that the earth is curving under.

let me give you a fact that a geography teacher can tell you about. if you go out 8 kilometers, that's 8,000 meters this way, you'll find out there is a five meter vertical drop. you will be 5 meters higher than you were over here. we live in a world that for every 8 kilometers you go out, tangent-wise, there's a 5 meter drop. that's all i'm saying. but that 5 meters turns out to be interesting, because we've learned something about 5 meters, gang, haven't we? what have we learned about 5 meters? let's suppose we take this laser, throw it away and we put a cannon, a cannon, newton's cannon. we'll put it right here and we fire a cannonball. is that cannonball gonna follow that straight, straight path? the answer begins with an n. hc? how come? because it's not beginning with a g. don't understand it very well

but we have it a little bit together. what is it called? - gravity. - gravity. gravity is gonna pull which way, up or down? - down. - down. watch. let's suppose i fired the cannonball at two kilometers per second. that means it will go two kilometers at a time in one second. so after one second, it's gonna be out this way. how far out that way? two kilometers, okay? two kilometers is gonna be out here. but it's not gonna really be there, gang. it's gonna be underneath there. how many people will be knowing how far underneath if it does not get in the way? beginning with an f, end with an ive. try it. - five. - five meters. it's gonna fall five meters. i don't care how fast you go this way, it's gonna fall five meters underneath, ain't that true? all right. so it's really gonna be like, well, like that. it's really gonna be right here. and if we're still gonna be air bound, i would have to dig a trench or something like that. gang, this is not the scale, yeah? it is not the scale. so it turns out my cannonball will follow the curve.

that's hardly gonna put me in orbit. i'm gonna hit sand. so i fired faster. i fire it at four kilometers per second, four. if i fire at four kilometers per second, how far out would it be in one second? - four. - you say it's four kilometers? but it ain't really gonna be up there. where is it gonna be? underneath. how far underneath in that one second, how far? see if you're sitting next to someone who knows. in that one second, how far underneath? is it still five meters? yes. it's still five meters. let's look at that. but you know what? the sand is in the way so you gotta dig. take a shovel, dig it out. the path would really be like that. in a little while, i'm gonna walk over here. i'm gonna put my arm right up here and i'm gonna ask the question, how many people in this room have calculated

how fast a satellite gotta go to orbit the earth. i'm gonna ask that question but not yet. let's suppose i fire this thing six kilometers per second, six. that means in one second, how far downrange? six kilometers. six kilometers, that's pretty far in one second. that's gonna be... [whistles] way out to here. is it really gonna be up there? - no. - no. it's gonna be where? - it's gonna be underneath. - underneath. how many people be knowing how far underneath? or how many people said, "i don't know." i mean, at six kilometers per second, i don't know that one. come on, how far underneath, gang? - five. - five meters. okay, so it's really gonna be like this. so i gotta dig. i gotta dig a hole. i gotta get that shovel again. now we're gonna dig. notice i don't have to dig so deep? now the path it takes is like this. let's suppose i fire it at 7 1/2 kilometers per second.

it's fractions. can you do fractions, 7 1/2 per second? how far downrange at the end of one second? - 7 1/2. - 7 1/2. that's about here, right? is it really gonna be up there? it's gonna be underneath. how far underneath? i still gotta dig. i wonder, maybe there's some speed i could fire whereby i don't be needing a shovel anymore. how many people in this room can calculate in their head how fast a satellite has to go to stay in close earth orbit? how many have made that calculation that newton made in your head right now? can i have a show of hands? eight kilometers per second, right? you're holding a book and a kid walks by and says, "hey, i see you be getting the college physics book there."

you say, "i be taking college physics, honey." the kid says, "maybe you can be answering me a question. "i always wonder how come the satellites don't fall down? how come they don't? you're a college person, tell me." you say, "well, it's all in the math, kid. it's all in the math." the kid says, "what's all in the math?" and suppose the kid wants to know. can you tell a kid why the satellite stays underneath? you can say to the kid something like this. "hey, kid, hand me that rock. i'm gonna drop it. tell me what you see." the kid says, "you dropped a rock, it fell straight down." "kid, i'm gonna do it again, tell me what you see." the kid says, "oh, this time you dropped the rock, "but it was moving when you dropped it. so it didn't drop straight down. it curved over." yeah. "kid, i'm gonna do it again. tell me what you see." the kid says, "you dropped it again. "but this time when you dropped it, "it was going even faster so it made a bigger curve and fell way down there." you say, "right on, kid. "now, kid, i got a question to ask you. "what if i move my hand so fast that the curve it makes

"matches the curve of the whole world, then where will it drop?" and the kid--poom!--he's got it. he's got it. he's got it. he sees it. he says, "it will never drop. "it will keep falling around and around and around and never hit the ground. that's all there is to it." and you say-- it begins with a y. - yes. - yes. and he says, "ain't it really get more complicated than that?" no. no. it's that simple. think about these ideas. see you next time. [music]