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do you know motion separating your ex from your Y well here we go [text on screen]

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as we all know motion can go in one direction at a time right wrong [teacher speaking to students]

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there is actually something called two-dimensional motion it's a little

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more complicated than a one-dimensional motion as you can imagine so up until

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now we've just been ignoring it haha but we can ignore it no longer in our [man jumps up to kick soccer ball]

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previous lessons we've focused on displacement in just one direction or [dog walking down path]

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one dimension to be precise the displacement could be negative or

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positive it might have been all vertical or all horizontal but it was never boats [eagle flapping its wings]

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in real life though we're dealing with more than one dimension let's say we're

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playing fetch in the park with our pet anteater Charlie when we throw the ball [woman throws ball in park for anteater]

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to Arvid to get we don't just throw it horizontally we've got to get some air

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under the throw also so we throw it up in the air but not straight up because

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all it needs his exercise so if you're thinking of this on a graph

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we've got displacement on the y-axis and on the x-axis - which makes it easier to [graph on screen]

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work with because we can look at the movement on each plane separately but

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before we get too deep into this let's make things even easier here on earth

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any motion has to deal with friction anything sliding on the ground has [train going by, anteater gets dragged away]

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friction think you can escape it - by rolling instead no the friction is [anteater riding in a buggy]

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different but it's still there even something flying in the air has the

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force of friction for working against it which is why most meteorites burn up [meteorite zooming towards earth]

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before they can hit surface but remember when we said we

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like simple things so for now we're going to forget about friction we're

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going to pretend it just isn't there don't worry all your friction fans we'll

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get into it eventually but we want to understand the fundamentals of motion

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here something else that will help us with those fundamentals we're going to

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assume that any horizontal motion is constant we're also going to assume that

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any vertical motion is accelerated by gravity and only gravity so when we

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throw a ball in the air we're not going to be graphing its motion if an eagle [eagle steals ball]

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swoops down and grabs it one important thing to understand is that horizontal

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and vertical motion are independent of each other

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what do we mean by that well let's do a little thought experiment say we're

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going to play a little paintball I'm gonna fire off a test shot to make sure

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nothing jams up when it counts so we line up the gun parallel with the ground

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completely horizontal if our friend lets a paintball drop to the ground at the [man with paintball gun]

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same height as our gun and it drops at the exact same time as we pull the [woman holding ball in hand]

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trigger which ball hits the ground first the one shot out of the gun or the one

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our friend just drops we might think that the ball that's shot out of the gun

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will stay in the air longer after all it's covering so much distance

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horizontally but in fact both would hit the ground at the exact same time and

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that's because the horizontal motion is completely separate from the vertical [paint balls splatter on ground]

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motion the effective gravity the downward acceleration is exactly the

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same on both paintballs so even though the horizontal velocity is completely

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different the vertical displacement velocity and acceleration are the same

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if you want to see this with a real gun and a real bullet the Mythbusters did an [woman watching tv from couch]

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experiment on the exact same things you can click on the link here to watch a

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consolidated version of the experiment verdict physics tells the truth but then

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physics always tells the truth that's why we like it so much as we've said

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vertical and horizontal motion are independent of each other but that [writing on chalk board]

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doesn't mean they're not linked what's the link between them time at any point

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in time we can describe an object horizontal or vertical displacement its

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horizontal or vertical velocity or its horizontal and vertical acceleration

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and the same equations apply to both direction but we'll rewrite them

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separately to make sure we don't confuse our X for our Y what are those equations

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we thought you never asked these might look pretty familiar we've seen them in

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previous lessons let's look at a simple one first we want to find the change in [writing on chalk board]

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displacement along the x axis to do that we'll subtract the initial displacement

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from the final displacement another way to find that displacement is if we have

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the velocity and the time in that case the change in displacement equals the

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velocity in the direction of the x axis that's why we have the V sub X here

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times the change in time if I'm looking to find the same thing in the y axis

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we'll just change all the X's in two y's like this if we're trying to find

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displacement but we have to deal with acceleration then do we have an equation

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for u in that case the change in displacement along the x axis equals the

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initial velocity along the x axis which is what V sub X I stands for times time

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plus one-half of the acceleration along the x axis times the square of the

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elapsed time it just trips off the tongue doesn't it and again when we're

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dealing with vertical motion which is going to substitute Y for every X even

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the subscripts okay one last equation to look at and if all these B's and x's and

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T's have your head spinning feel free to take a second to clear your head but [student with equations dancing around their head]

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we're going to be using these equations like crazy in this unit so as you

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Americans love to say that go up okay so this is what we'll use to find the final

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velocity along which have access if we don't have info on how much time elapsed [writing on chalk board]

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but we do have info on final velocity displacement and acceleration so the

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square of the final velocity along the y axis yes that's right when mixing it up

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on you leading with the Y motion this time equals the square of the initial

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velocity along the y axis plus two times the acceleration along the x axis times

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the change in displacement and this is what it looked like for the

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x-axis rather than the y-axis it just looks X yeah and it's important

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to recognize that we can never ever ever put X's and Y's in the same equation the

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dimensions have to be kept separate which sounds like something from a

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monster movie but this would result in something worse than an interdimensional [t-rex chasing X and Y]

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monster it would result in the wrong answer that's really scary so let's put

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these equations to work shall we and we'll start with something we'll are too

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familiar with falling down anything that's in freefall experiences

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acceleration in one direction straight down that's gravity for you and that

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doesn't matter if we take a wrong turn and drive off a cliff or if Steph Curry

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takes a half-court buzzer-beater in either case we have velocity along

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the x axis but the only acceleration will be along the y axis with no

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acceleration that horizontal speed will stay the same forever well not forever

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forever but car will be coming to a sudden stop before too long this type of

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motion with acceleration in the Y direction and the constant motion in the

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X Direction is called projectile motion and when we have a projectile motion we [graph on screen]

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get to assume acceleration along the x axis is 0 meters per second squared and

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the acceleration along the y axis is negative 9.8 meters per second squared

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when we have a projectile motion we're able to get rid of some of those [writing on chalk board]

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equations we looked at before we had six equations three of each for x and y but

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since we don't have any acceleration along the x axis we only need one

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equation for that motion we'll need the one for the change in

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displacement along VX which will either be the final displacement minus the

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initial displacement all the velocity times the change in time since we do

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have the acceleration in the Y direction we'll have a couple of equations that we

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can use for that motion first we have this one where we'll use the velocity

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the acceleration of gravity and and if we don't have the elapsed time we

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can use this one that certainly cleans things up for us

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if we have constant acceleration in one direction and constant motion in the [basketball game]

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other we end up with a parabola just like that sweet Steph Curry jump shot

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hmm we can see that represented here here

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each basketball represents an equal interval of time we can see that the

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speed is much faster at each end of the graph and slower at the top here let's

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add some arrows to make that clearer see how all the horizontal arrows are the

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same length that's that constant motion we keep

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yapping about and the vertical arrows those are the same length or magnitude

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at each position along the y axis it's just the directions that change going up

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for the first half and down for the second half it's like the first half has

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an evil twin in the second half of the jump shot so this is a graph of the

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motion combining the x and y motions but we still have time that's binding them

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together what would the graph for the motion in the X direction looked like in

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terms of time funny you should ask we just so happen to have the graph

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right here see that nice straight line that's constant velocity if we ever saw [graph on screen]

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it just like we'd expect when using this equation and for the Y motion in terms

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of time boom another parabola it's like poetry in motion or poetry in a motion

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equation we're not going to lie two-dimensional motion is more

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complicated than one-dimensional but as long as we keep x and y separate we

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should be able to handle it just fine after all it's just a matter of applying

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the right equations to the right direction and we've worked with these

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equations before so we know we're up to the task

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let's just be thankful there's no such thing as

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dimension

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