Physics - 2D Kinematics - Vectors in Two Dimensions | Corey Mousseau | Skillshare

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Physics - 2D Kinematics - Vectors in Two Dimensions

teacher avatar Corey Mousseau

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Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

Lessons in This Class

4 Lessons (53m)
    • 1. PhysicsCourseOnline

    • 2. 2d Kinematics 1 Vectors 1 High School And Ap Physics 2

    • 3. 2d Kinematics 2 Vectors 2 High School And Ap Physics 3

    • 4. 2d Kinematics 3 Vectors 3 High School And Ap Physics 4

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About This Class

Physics is all about the world around us.  We live and experience physics every moment of our lives.  For most, we take physics for granted and never really truly understand how this amazing world works.  

This course is the next in a series of courses covering the physics topics of One and Two Dimensional Kinematics. 

One of the most important concepts in all of physics is vectors, especially vectors in two dimensions.  I will walk your through this challenging concept along with plenty of examples.  

You should complete my prior courses in this series before completing this course.  

The complete order in which my courses covering 1D and 2D Kinematics are as follows:

To be honest, I fundamentally believe every single human should have a basic understanding of physics.  This is especially true for anyone working or aspiring to work in any field even remotely connected to the STEM world.  This includes obvious professions such as scientists, engineers, and doctors, though also include many surprise fields such as law enforcement, athletic anything, computer science (and all related fields), law, animation, and much more.  

I am a high school physics teacher by day.  I create the majority of my videos for my own students.  My courses all follow NY State high school physics entirely, as well as the nationally renown AP Physics 1 & 2 curriculum.  AP physics is exactly the same thing as any algebra based college intro physics course.  

If there is enough interest I intend to share out all of my courses which cover all of the remaining topics associated with AP/College physics.

Meet Your Teacher

Physics is all about the world around us.  We live and experience physics every moment of our lives.  For most, we take physics for granted and never really truly understand how this amazing world works.  


To be honest, I fundamentally believe every single human should have a basic understanding of physics.  This is especially true for anyone working or aspiring to work in any field even remotely connected to the STEM world.  This includes obvious professions such as scientists, engineers, and doctors, though also include many surprise fields such as law enforcement, athletic anything, computer science (and all related fields), law, animation, and much more.  



I am a high school phy... See full profile

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1. PhysicsCourseOnline: Are you interested in learning all about physics? Do you want to master the high school in AP curriculum? Whether you're a high school student or an entry level college student, this course is for you. Each syriza dresses every topic thoroughly with lessons, demonstrations, an example problems. 2. 2d Kinematics 1 Vectors 1 High School And Ap Physics 2: Yo, moose. So here, let's talk about vectors a little bit more than what we already have. This is all about vectors, OK? And we're not even going to toss down too many other concepts other than straight of vectors. But of course, with vectors is give me a lot of well, you'll see a vector. Remember, anything has magnitude and direction, right? Way off to represent vectors, these of the Euros. We already talked about this. You've seen this a couple times, so that was nine units long. I don't care what this is. Some vector for the sake of simplicity. Label it right now, but it could be any vectors. Could be velocity displacement. It could be even forces things we haven't learned yet. I'm gonna head. Go ahead and say the velocity here. Just the legal it is. Nine units will say nine meters per second, uh, straight for we've got that, Demery. I can draw another vector. That's only three units long, and you can tell Visa vee their proximity in size that indeed this is smaller and we already measured it. It's long, easy stuff. This is straightforward basic factors. When I need to talk about today is how to add vectors, how to put them together when we're talking about one dimension. So if I were to draw a my cardinal axes here, or maybe even we can consider this a coordinate system X and Y I don't care if we're dealing with just one dimension vector addition and subtractions various straight forward. It really is a simple as addition and subtraction. So it's good that divine it's good to define positive versus negative. And if you don't actually define it and we're gonna treat everything to the right is positive and everything to the left is negative. So I'm gonna go ahead and do that. I'm going to say that this sucker is positive. Nine meters per second. If I would event, let's say this is a car traveling and then it experiences an additional, maybe when boosting it from behind three meters per second. If I would, I'll draw this off to the side first. I would go ahead and have that three meters per second velocity vector that I had there before. I want to say ask you now. Well, what is the final speed of the car? So I'm getting a little bit ahead of myself. First and foremost, this is initial speed of the car. This is a speed that's being added to it since it's being added to it. Since it's behind the car, it's getting boost it so we could do this Arithmetic Lee by just taking nine plus three. You know, it's good B 12 meters per second. Cool. We can also show this graphic week by taking this vector in placing on top of this vector in method that we're gonna call that that's called tail to tip. So let's talk about the vector itself. The base of the vector is the tail the arrowhead. The end of that arrowhead is the tip an easy way to graphically show. How we can add these two vectors together is the place the tale of one vector such that it ends at the tip of the other vectors. So there's a few things needed to know about vectors. Vectors can slide or translate anyway. They want. Okay, I can take this guy and place it over here. Place over when you drive. Vector doesn't show where the object was existing. It just shows the actual magnitude and direction of the vector itself. I cannot rotate the vector cause that's changing the direction That's bad. And I can't stretch it out or shrinking because that's changing the magnitude. That's bad. But Aiken slight it anywhere I want. So if I would actually redraw this three meter per second vector such that its tail finishes at the tip of this one, I made you that quick. Can't be too. And this will be the one to say confused myself. Now that they're both on top of here, I confine what we're gonna call the resulting vector or the result inked Vector. What is the sum of these two vectors together? We already did it using our basic math nine post to use 12. Let's do it. Using the graphing method Elway, I do. There is measure how long this this vector itself is. This factor is 12 units long. So I'm gonna draw this again down here just so we can see them away from each other. It's fine. A drawing on top of it. It's not really a problem, but I'm gonna draw the resulting vector. I'll do that in a couple. By the way you see, I have new markers. And we have a few colors, though, so help represents a red and use my old market, which I don't really like or or someone my different hues of blue. These metal markers also don't like and my purple is pretty cool over there. But I've also got this lighter purple so I'll use some of these markers, but they're starting to fade. I gotta upgrade even more, Really? Should just get with 1000 different markers. Give me too many options anyhow, So I'm gonna drive myself 12 minute long hair a burnin, burnin, burnin, burnin am There it is. Ah, and because I measured it as 12. I know this is told us per second, so my overall, the which sometimes we don't subscript at all. Sometimes in my public of E t or total, Mr Levy is simply 12 meters per second. So that means this car that was going nine that experience of wind behind it of three will finish at 12. Easy stuff. Right and subtraction is pretty much the same way. But sit, I guess I don't know. It's where we take that vector. So let's say this wind was now pushing against this. Something changed my arrowhead. So it's still three meters per second. But now going the other way mathematically under defined. This is positive. This is negative. So it'll be just nine minus three or have a final velocity of six meters per second. Acted against it, right? But we can also draw this again using the tell the Tipp method. I'm going to redraw that vector on top of the tip of my old vector. So the tale of my original vector will start here at the tip of the black character and it's gonna finish great here. Okay, so the black vector is my original nine, minus that three velocity of Meisel label right up here to this three meters per second. And since I have that arrow, is Jonah left? I don't need the right negative in here, but it wouldn't be a bad thing if you're negative. So now I can measure my overall resulting velocity is once again it's looking that six units on so I can draw this. It's still to the right that it will still finish to the right so I can drive us here 16 years long. So my final velocity in this example is simply six meters per second. That's not too bad. That's pretty straightforward stuff. You're likely not gonna graph one dimensional vectors because it's just basically arithmetic, really, where the graphing method comes into place when we have vectors in two dimensions. Let's give you the bulk of this video is two dimensional vectors. What happens when I have And I'm gonna teach project emotion in a completely different lesson. But what happens if I take a ball and I project it? Okay, if I throw it across so one dimensional motion, I roll it across the surface or I throw it straight up in the fall. Straight down, that wasn't street was up and down. That's also one dimension. It's just in this dimension. So this to mention this, what happens when I give it two dimensions? What happens when a as a projectile? Okay, perhaps you can see here that it's traveling in both the left right dimension and the up tenements. It's hard to actually demonstrate this, because the top down view of my camera, if I would actually show a project I'm motion looks like it would be this parabolic path right. And I could always turn the camera and throw it across the room. I think you guys know what a ball traveling across the room looks like. So I'm gonna draw that vector is a vector at some angle. I'm going to say that this vector will you give us it? We'll use a real protractor and everything. I'm going to say this vector eyes a 30 30 degrees above the X dimension, the whole plot, their little plot there, Um, next 30 degrees. And I'm gonna make it. I don't know. We'll make it nine units long. Just like the last night. I'm gonna get this ball nine meter per second velocity at some angle above the X and any measure that will be 30 degrees, right? This is the vector in two dimensions because part of it exists in the X dimension or the horizontal dimension, and part of it exists in the UAE dimension. So, a new thing that we've gotta learn well, first before even get into how toe draw the vectors. Ah, a rule to learn whether it's for velocity or forces or mo mentum. It doesn't matter any vector, uh, the two dimensions are independent from each other. The X dimension does not affect the Y dimension why dimension does not affect the X dimension. They will come together to make my overall velocity vector momentum vector for Specter. Whatever it is, they will come together. But they are independent of each other. So we're trying to predict its motion like where the ball will land. We have to consider on Lee the X and on Lee the Y separate from each other and you'll see when we get into actual project Emotional For now, this will show you how to draw these vectors. So any time you have a vector angle, any time you have a vector at an angle, you could always draw in what we call the component victims. The component vectors are the vectors that exist and solely the X dimension and solely the why to mention or if it's like y and Z just solely those two dimensions. Okay, so this is what we're gonna label as the sub ex my ex velocity off this nine meter per second projectile and this is visa ready for it. And he said, Why? That's the why to mention so my why component, my ex component come together to make my overall velocity vector of nine. So how do I find out what these two vectors are? I mean, if I know the nine meter per second horizontal or not horizontal high pot news, By the way, this is known as the only write these in this guy, the one that's at the angle. This is known as the resulting vector or the resultant, and it is the result of these two vectors. So these guys are known as our component vectors. We could call this the X component, and this is the Y component. Any vector at an angle will always have to component. Got will always have two components that come together a 90 degree angle to make a performance. So the X and Y components will result in the 90 meter per second vector. So how do I calculate what these two vectors are for that? We need to go back to a rate triangle trigger basic rate, trying a trick that we may have learned in math at some point in time. And if you haven't learned it yet, nice and straight for nice and simple, there's a little rule here. If you know to values of any of the six of a right triangle, you can find all the rest. So we have our had pot news on our two legs, and then we have a 90 degree angle in our two interior angles here. If we know two of any of these, we can find all the rest. So we do know, too. We know the hypotheses, and we know the angle. So there is this thing gonna rate out here that a lot of teachers right out called soaking toe up. Now, I'm not gonna teach trigged right now because, well, this is a physics lesson. So if you need more help on this, I encourage you to check out some extra resource is on that YouTube is your friend. But for now, I just get a rate out. So could tell what kind of write down what it all means and then show you some map on how to find my X and my Y components. Right, So? So that stands for if we were to say the sign of some angle. So the sign of my angle theater s sign equals my opposite leg of that angle, divided by my iPod news. So sign equals O over each, and I'll translate this to my example in a minute. Co sign of some angle. The car is my adjacent leg, divided by my environments. And then we've got the Totowa. Do you know, struggling too many options lineup popped into. My gosh, I'll do it. Read the toe apart says the tangents of something will seem like the other ones. Barracks of finer tip. I'll go shopping The tangent of some angle Feta is equal to my opposite leg over the adjacent Cool. Remember this? This is true All the time. Any time we have a right trying, I remember trying with a 90 degree angle in it. We can use our right triangle trigger so could tell him we could use their fancy calculator to figure out some values. So I'm gonna use this in the terms of this example, you define my components X and Y protected. Get away. So, um, I need a little bit more space. Some of the theory of the components Sultan beverage trying. Go there. Give us beauty music. I want to find X and y before I do that. Sure. I could also find my angle in here, right? Because of the almighty. Add up to what value? What value of 180 degrees of 90 plus 30 plus X. Give me 60 or these two always have to add 90. So 30 plus four equals 90. So that's 60 but I'm not gonna need it. I'm gonna use this. Is my Anglophilia ready? Let's just do this. I'm going to say the sign of my angles. Data. So sign of 30 is equal to my opposite value over my iPod news. So it's giving equal to my opposite valley. That's an unknown there. The sub y I could put X if I want to, or Oh, I prefer to put the physics variable there. So everyone doing over my high pot news and I'm gonna leave in the variable format first, So would be signed of data equals V lie over V. And I guess if I really wanted to particular leaving in my variable form first, I'll just do this. A sign of Fada equals vo Overbey. And maybe I'd call that fate a one because this would be probably eating too right now. I know. I know. If they don't want, that's 30 and I know V. That's nine. Could write that in data one is 30 degrees and V is nine meters per second. So I want to isolate the y. So I'm gonna multiple. I'm gonna carry that V over to get view I by itself the why will be the time to the sign of my angle theater. This is a pretty typical set up. We typically, once we get used to our trig jump right toe this line, we don't start here. I'm just doing this. You can see where it comes from, but often will say the Y component is equal to view time. Some trick value and the X component is equal to b times some trick value. So in this examples, give me the nine times a sign of 30. Now I understand. I know what sign of 30 is pretty quick in my head. I'm gonna go ahead and use the calcula just so we can show you how to do that. I like these graphing calculators. If he's a scientific, you might need to go backwards. Might need to do the trick first and then multiplied by the nine. Just nine times. Right? Magical rate. 97 30. And you don't even have to close that. Parentheses is just having to do it and oh, wow, that's way wrong, right? That's negative. That's crazy. How come that's like that? Don't write down some absurd value. You know it's not negative. 8.89 is appointed that way. Where I'm sorry. This is The wiring is appointed down. Negative is down. Know something's wrong. Let's go in my mode, that's what it is. I'm in radiant mode. You go over the degree. Always make sure alligators and degrees when you're doing tricks. I'm sure your math teachers have hammered that in over the years. Right? 4.5. That is so much more logical. So 4.5 meters per second. Also itself woman know that sign 30 is 1/2 cool. Now we know of you wise. 4.5 meters per second. Now I could then go ahead and do Pythagorean theorem to find the exes. I know a squared plus B squared equals C squared. If I know C and B, I could find a I'm not gonna do that I want to do some tricks just to show you how to do it . So I'm gonna go ahead and say the ex were No, actually, let's go. I'm looking for Vieques. What, like is this? This is my adjacent leg. Because remember, Although there are two legs adjacent to this angle, Jason needs next to it. This guy's my iPod news. I partners always along this one the one opposite of my 90. So the other leg is my adjacent like this is a So I have a or I'm looking for a I have hte my iPod news I'm gonna use co sign were most often using signing coast on your rarely We use tangent That's a little heads up. So the coup sign of my Anglophilia is equal to my adjacent value The X divided by my news the and the knowns air still true Gonna get Vieques by itself. The X is equal to multiple i v over the coast data. And again, this is typically the way we start these problems off. We don't start here. We start right here because we know this is true. So these would be nine times the CO sign of 30 co sign of 30 is not 1/2. There is a coast function that you can remember. Just go ahead and take it in. And here, nine years, 30 7.79 meters per second. Around that up to eat rock on its positives was to the right good. Those of my X and Y components. Easy stuff, right? Might forget some of this easy stuff. So I encourage you to practice this. You don't forget it, but that's all you gotta do for, right? Triangle trick with vectors now, there are Of course, there's more to this. And I'm going to do another example in vectors in the next video. Uh, right there you have it. Cool. I'm gonna in this video, and we're gonna just do more vectors in the next video. Thank you. 3. 2d Kinematics 2 Vectors 2 High School And Ap Physics 3: all right, Luso here when you do a little bit more in vectors. So in the last video about one dimensional edition, I found out once we have a vector at an angle, how do we find the components? Now I'm going to say I have two legs or victories in two dimensions. How do I have been together on And I'm gonna show you a math through and then literally graphing rule. And I think we try to do it side by side. Who names, We'll see. So I'm gonna tell you that I have a almost a displacement for this example, and I'm going to say that I traveled east, So d one is gonna be nine meters east. I'm going to say D two is I don't know. We'll go 16 meters north, okay? And I want to know what is my overall displacement? What is my final displacement, or what is the resulting value of these two? Right? For both a minutes for both the math and the graphic. I'm just gonna sketch it the graphing. I'm going to take more time to use my ruler with it, but for now, I'm just gonna schedule there say traveled nine meters east. And remember, if I'm doing tell the tip, I'm going to start this next vector. So just tail starts at the tip of the last. I'm gonna draw this one 16 meters north. This is a sketch. These air not to scale. That's okay. Now, technically, I could have done 16 meters north and then nine meters east. I'm gonna finish in the same location, so factors don't really occur in a timeline. The a word problem will logical to know that you went used in the north is the north and the east. But your final destination will be the same. Cool. All right. Hopefully you recall displacement. My final displacement is the direct shot from start to finish. So as if I didn't do nine and then 16. But instead I did this and see here this is my resulting vector. So once you have two components, you resulting vector always starts at the first and finishes at the last. Excuse me. Sorry about that. So you're resulting vector. Always start to the first and finishes at your last. Would you have a right triangle? So we're gonna use right triangle trick. I want to figure out what is this value for that? Mathematically speaking. So the math roots as long as we have them, John, to have a tip in it many degrees Weaknesses by thank So Pythagorean theorem I'm gonna do. And I say a squared plus b squared equals c squared. Or in this case, I'm gonna say D one squared plus d two squared egos my overall d That's the right way of writing in terms of physics instead of in terms of matter of the map, Rude isn't wrong. Oh, sorry. D squared so d will be the square root of D one squared plus d Do you swear? So I just get a plug gunning down here. De Juana seems to be nine squared plus 16 squared. Then we're route that whole saying, Let's process of my calculator. So I'm gonna go on and say nine square plus 16 squared and then I'm gonna root the whole thing, right, and I'm gonna get 18.4 years. Awesome. That's the math room. The graphing route. It might be a little bit more time labor intensive, but it might be the easier ruined. A lot of times you have to do the map the graph route. Anyhow, Even if you wanted him at the problem, it's simply say, using a graphical means if it doesn't specific. So you get the pick whether you want to math or graphic. And so the graphing way we have to set a scale here. And I'm gonna go ahead and say one meter is equal to one centimeter. That's nice and easy. I can just do a nine centimeter long vector bam! And now I'm going to redraw these two vectors over here. I guess I won't do purple. Er makes it up, right. So I'm gonna go ahead and draw a nine centimeter long vector. I gotta give her my borders when I think I'm gonna do, Huh? I think I might need to do that. But in these rulers on your snap, my really happy I suppose I could do that, man. So anyhow, nine centimeters will represent nine meters se de one is nine meters and then I'm gonna draw the other vector such that it starts at the tip of my last specter. And I try to keep this so it's perfectly vertical and that was only open 16? Way up here? I guess I should slide this thing. All right, All right, all right. We do. We repeated bebe me do this down here. Maybe she did a 16 meter one first. Yeah, I'll do that. Even show that you can do that yourself. So I'm gonna draw the 16 year nor effect instead. One, it will help me cease under identifying my space and to It'll help me show you. It doesn't matter if I want to use the north of north. And then East Perfect was meant to be. Now, that's what they call a teaching moment, I guess. All right. I know Willie Lane. I'm just think so. You guys okay? Uh d Well, I'm still gonna cause D to just because it corresponds of these values. Appears a D two is 16 meters and d one is nine meters, and once again, you're resulting vector. Whether it's a sketch or not, we'll always be starting at the tail the first and finishing the tip of the last drop this way. And then I measured after I like to draw my results as dashed that way it helps identify that it's not a new vector. It's replacing these to see the do your components dashed or your resulting dash. But don't do all of them Seller off. Um Dash. So how do I figure out what this is? Simple. Just measured with your rules. Take my ruler and place it down here and I'm going to see here that this is Oh, I don't know. 18 point. I'm getting roughly 18.6 or so. That's it. I just figured it out graphically. Now I left something out over here, and over here on purpose, I'm gonna show you both of them in tandem because when we're dealing with final, resulting dies of vectors, the magnitude isn't enough. You gotta remember vectors require both magnitude and displacement. I'm sorry, Magnitude and direction. So I need to understand and identify the direction. So for that, I need to actually calculate my angle theater or measure my Anglophilia. That could measure this one and then subtracted from 90. But I'm trying to make it be the same angle for both of my triangles. So I'm gonna show you the math route and then we're sure the graphing OK, so what's my angle? Dada is inside this right triangle Now I have all three legs. I didn't write my number down, but it's right here. By the way, you notice these numbers aren't exactly say which one you think is more accurate. Math of the graph Math of the graph. The math is more accurate using concrete tricking a metric values here, over here, you're measuring with a rule is a degree of error in there, right? So for more accurate result, always use meth in an event. Trig is what we gotta do. You too find data. So Cortona, I know multiple legs. I'm gonna go ahead and use the legs that were given instead of like that was calculated That way. If I haven't error down here, I won't have an error over here. And I'm going to see that I have my opposite leg and I have my adjacent leg number. So Krakatoa, which one uses opposite in a Jason and that's toe, uh, or tangent something. Said the tangent of my angle. Fada is equal to my opposite value 16 meters over my adjacent value. Nine years. So if I were to take this in my calculator, I'm gonna find out that Tangie. It's simply 16 divided by nine or 1.7 repeating. So the tangent of my angle theater is one point seven repeating. Is that what I want? I want 10 theater or don't want feta. Yeah, I want data. Sophia is always going to the inverse of my trig so inverse tan of 1.77 So I'm going to see that I'm gonna say, second, my inverse or the second numbers he sees a little blue on top calculated might be slightly different. Second, tan not gonna carry this answer over. So it's a second answer, and that's giving me an angle of about 60 degrees, 60.6 degrees. So I'll say 61 degrees Sweet. We're gonna measure it now. This is one a lot of students doing, cause for some reason, they're confused on how protractor works. Best way I can try to explain it is Think of a protector is half a circle we know circles. Three engine, 60 degrees. So this represents 180 degrees. He's out of numbers, is just simply 180 degrees is a zero started here, and the interior numbers air 180 degrees as well as if he started here. There's a little cross here. It's always good to place it on the cross hair because now it could split this in the quadrants. This would be quadrant one, then two. Then three would be down here and four would be down here. So this is 0 to 90 or 92 0 However, you want to think about it. So I like the place. My honestly keeps a calculator or your protractor many, many different ways. I like to place the crosshairs right at the base of where my probe. My angle. It starts to realize that this is my horizontal line and I want to measure this line. This angle right here, Sanders said this being 0 10 2030 40 50 looks like about 60 degrees, give or take a degree, because the thickness of mine marker. If I started here, I would go 20 to 1 80 So I just gotta do some math and subtract. I don't encourage you doing that kind of my initial when a B minus 1 2060 you know which way you're gonna get 60 degrees, which is dangerously close to the bathroom just like it was before. So measuring an angle is actually very simple. Saves you some math ears. I mention this to be 60 degrees. Gnarly stuff on last bit. To go with the angle is also directional information. Since I knew this was easy and this was North, I've got to say that this is 60 degrees north of my east line north of east, which is different an east of north. So I still have some time left in my video. Let me kind of go over that a little bit more once they raise my board. First, digest this about the race, this board positive, and you look at it again. Cool the race. All right, real quick. I just want to get into that hole Cardinal direction stuff when it just over exaggerate. I'm not measuring to be dead center. So if this is a little life Duncan to man, I'm just used to in class. When I draw these things in front of students, just a police one kid that was like That's not perfectly standard, and it really drives their brain nuts for that. I apologize. So here's my North East now up in West. I just want to quickly and I'm even get a free hand. It I'm gonna say I'm gonna have my vector like this is Stanley. Say this is 40 degrees and then I'll say this is 50 degrees, so this vector could be described of one of two ways we can say this vector ready for this is 40 degrees south of the east lines you were easily He went 40 degrees south of that. So this could be described as 40 degrees self of east or ready 50 degrees just east of so because he went 50 degrees. He said they're the same spots. Hence, if I wrote 40 degrees east of south, it would be wrong. That would be a little bit too shallow. Give another example up. Here we go. Real steep. Say, Mrs 20 I'm just eyeballing it naturally. Which means this would be 70 degrees, right? So we could discuss this as 20 degrees. Well, what did I do here? 20 degrees. What? Yell it sold out. So I can know. Okay, It's that work. I guess I can hear you 20 degrees west of north west of north or 2070 degrees north of West . So you have a compliment, baby. Opposite regions. And if you don't know what Northeast herself, whatever you can say 30 degrees above the X axes 30 degrees below the X X is or 30 degrees to the right of the Y axis. If you really, really, really, really, really want to get down to it, 30 degrees always means this. If you don't say it, it doesn't mean this way. This way, this way, this way. So then this would be do, do, do, do, do do do do so. If I had 30 degrees here, this would be 90 lost 60 So this is technically 150 degrees. So if you don't define direction you go three year old school math or your current school math. I don't know. 0 to 90 to 1 82 to 73 60 right. Made us work you again. People that hate imperfection. I'm sorry, but all the little blemishes there, But this is what I'm doing. You deal with it. I can see. I can hear some of your yelling. I know I can. It's definitely happening. So instead of it being a kernel system, do coordinate system zero degrees. This is 90 degrees says 1 80 to 70. So for to tell you something was down here and have to respond on this is also reinforce 3 60 I'd have to given angle between 2 73 60 So far to say 280 degrees is 10 degrees more than two seventies. Here they don't necessarily have to define left or right or above or below 87 e without any reference of directions. Always here, Celestin. Between 0 90 So this is always 60. This is always, I don't know, 90 plus will estimate that as 70. So 19 seventies is 160 degrees. Which would be that one. This other one was through this line here. Got it. I think this makes sense. I don't know. Maybe I made it confusing for you. Okay, We gotta do one more video on Vector Edition and angles and all that stuff. It could be a pretty complex problems. You can see kind of the most extreme case on how to solve vector stop homes before I get in to project on motion. Sweet. Thank you. 4. 2d Kinematics 3 Vectors 3 High School And Ap Physics 4: All right, So this is gonna be advanced problem on vector addition. When he's a displacement example, you would never be asked to do this on, say, a regents exam. But certainly you do need to understand every aspect of it. This certainly could be something that has found its way into the classroom exams or into, ah, college level course. But this is not beyond any level of physics expertise. Just give me a little bit more complex, and you probably would have to do, but it will help. So this could be a displacement problem. And what I'm gonna do is I'm gonna just kind of give a running value of stuff down here, and I want a graph it out. Then we're gonna math it out. It's getting crazy. All right, I'm gonna say, and I'm ready to go with displacement. I'm gonna say a person started and they traveled six meters completely east. Then at the end of that, they traveled. Um, I don't know. We'll say four meters on an angle of 30 degrees south of east. Then they went, Oh, I don't know. Eight meters man will say 45 degrees southwest, and then we're gonna say they traveled north. Another 11 meters was completely north. And then finally they finished. We're traveling. Additional five meters are an angle of 20 degrees. Use the north. I want to know what is their final displacement. And often the way we rate final. The way we do result in its and I haven't shown this yet. Any videos is using the Sigma symbol. What is the sum of all the displacements now? A lot of you remember Signal stands for some of all, but you wouldn't intentionally just add it all together. It doesn't just mean add everything as if they're in line with each other. Can't forget there in more than one more than one dimension. So now I'm gonna graph this out, we'll show you how using graphing skills might make this problem easier. But then I'm gonna break down how to do it mathematically. So this is to be difficult for me to do first run. So if I screw up, I'll have to just fast forward through my error. Maybe when I go to meditator come back, who knows? So if you don't see one little really fast shortly, it means they did it right the first time. It's just because I'm trained. Envision. OK, so I went six meters, and then I went south and east, and then I went south of west than I went north and then went east. I don't know. So I'm gonna try to start way over here. I think I'm gonna finish up here somewhere, so I'm gonna start right here. I'm gonna draw, and I'm gonna treat one meter. Did you write that scale? Down one meter is one centimeter. And so I'm gonna start here, and I'm gonna say I went six meters east. Then I went for four meters, 30 degrees south of east. So what? That spot. I'm gonna take my protractor on a place it right here, going south sides. Why? It's upside down. This is easy. This is doused south, someone 30 degrees south of these. So I'm gonna go this way. So I'm gonna john my next vector in line with that top. But I don't think it's give me that long. We should use a permanent marker in this problem, But I don't really feel like subpoena about to clean my board in, so I'm just gonna press a little bit lesson on here and that needs to be four units. Mom, notice how I'm following my tail. The Tipp method. Start the tail. The tip of the last that I'm going to do eight meters 45 degrees south of west. Some was going south again. Something down this way. And this is the West Lines. I'm going 45 degrees this way. That puts you in line with that dot Right there? Yeah, they're gonna be all right. It's not gonna be perfect. Perfect. Perfect. But I think you're gonna get the idea that needs to be eight meters long. So eight units known. They tell the first or the tip of the last at the tail of this one of the typical last one . And then we're do 11 meters north. So up here, hopefully I don't run into my skill. And I really doesn't want to be positioned that way. So I'm just gonna start. I'm at the 15 centimeter marks. I need to go 11. So I need to finish What? Yeah, 15 miles 11 is for Okay. That's where I am there. Damn! Since 15 earned 11 meters and then finally I'm going five meters, 20 degrees east of the north vectors. So 20 degrees east of north, I've gotta find north, and I got 20 east of that. So it's actually over here of the 70 degree mark, 20 degrees east of north. So 90 minus 20. And so this last factor needs to be five meters that way or five centimeters. That way, Mr Fine. Not too bad. I think I got this all right. They could fit it all in. I doubled my skill. Make this even bigger. I'm not do that now. I've done it. All right now, graphically, this is actually pretty easy to do off course. As long as I don't screw up my marker job. Can't do this. And Green and Dash this answer. My graphical is always gonna be the tail. The very first there should the tip of the very last. So I'm gonna start here and draw a line there. That's it. And I also want to measure that because that will be scaled back to figure out my value neither. So it's it looks like about 10.6 or so. I mean, not my markers. Little fat. Someone want to be a little off here. If you're doing this at home with a pencil. Probably a lot more accurate. 10.6 centimeters. So my net displacement is 10.6 meters and remember, always gotta find directional information. So you tosser protractor on there and we're gonna measure this single rate. Here is this is holders on the line and I'm looking at about 56 degrees yourself. So this is at an angle of 56 degrees, and that's north of East Cool. That's the graphical way it's done. Like I said, the graphic away on these complex ones tend to be a little easier because all you gotta do is measure with a ruler. Now I'm gonna do the math roots, math it out to math it out. This is very, very important. You could be doing this a lot. Never combined your ex values of the Y values. So to do it the math route, it's really good to create what we call an X Y table or an east north table. Whatever you want to think of it as meaning, we have to write down everything that's in the X here and everything that's in the UAE here and the things that are in two dimensions, we have to find the X and y. So it's like the very 1st 16 meter factor east that's purely in the X East is positive. So I'm gonna write D one right here. It's positive. Six meters now, D two, which was this guy here? That's four meters south of east. So we know part of its eat in the X. But part of its also in the wise is why it's give me important to find my component. I'm gonna dash in my components right now so you can see this 90 degree right triangle right here. I need to find d two x and D to why? And I need to find my angle. Data are not forming off the main use lying something. Do the math right here. I'm gonna say D two x You see how it's a decent to my angle theater? It's next to that angle. I hope you can see that. Jesus. So, Kat toe, uh, I have had partners. What trick value uses the adjacent as well? Yes. Coup son. Ready, he said. The rating out CO Santa because blah, blah, blah, blah I'm gonna say d two x equals d to times kill same theater which is giving equal to four co sign and 30 degrees. And it Well, well, 10 seconds of four co signed 33.46 meters. It's pointed to the right, So it's positive. So now I'm gonna write d two x this 3.46 meters. Naturally, though, I still have a part of detail left. I have de to lie here, So I'm gonna find that De Tu Ari is opposite of my angle. Fada something you sign So tow us so opposite my part news. I could use tan but then I'd be using a calculated value and I try to avoid that. So I'm gonna say D to sign data or four. Sign 30. Remember saying thirties 1/2 someone happened for simply two meters? If you don't believe me, put it in here. I'm not gonna do it. And that's why and what? Look at that shit's down. Don't forget that this is actually gonna be negative. So d to why is my first y value and it's negative. Two meters sweet. I'm gonna erase this so I can keep using the same space here. So positive you didn't get this down. All right, I'm gonna do in tow a slightly double time now, green. Uh, now we're at eight meters. I see it's in two dimensions, so I'm gonna have to find my ex. And why Components? I know this is 45 degrees south of West. I don't care where a drama angle. Just do it in here. It's 45 so I need to find D three y and d three X. It's also good to know that this one's down. This was left. It's the bulky to be negative. I'll do. I'll do X first D three exits opposite of my angle. Fada. So it's give me D three sign Fada, which will be our eight Signed 45. And that's to be 5.66 meters and again it's left, so it's negative. So d three x is negative. 5.6. Now I'm gonna go ahead and write the other line out, but there's something that some of you probably already see right now, and it has to do with that angle what I would do it and show it instead. So d three Why? It's a date adjacent to my Anglophilia and I have my partner something Use Cosan. Let's give me eight Coast 45. Let's toss it in my calculator 5.6 is what we need a second. Did I do it right? You had to do right? Yeah. Okay. I'm just playing silly. It is the same value because 45 degree angle the legs are equal to each other. Keep that in mind. So you're 45 saves a map. You don't actually bring it all out. It's down. So it's negative. So d three, why is negative? 5.66 meters sweet again. I'm gonna erase it and continue. So I have some math space and looking down at d four and I see D four is purely in the Why Awesome! 11 meters north. Positive. Cool. And the last one D find is in two dimensions. So once again I've got to find my components. Do some Triggs. Let me do that. Don't do that Black. I'm all over the place. My colors right now on that was 20 degrees east of north, so I could do this year but there's a lot of stuff going on. Something to do this guy in here. So I'm gonna say, Did it it it it it it it they did it. It it it, it, it it it. And so this is D five X and this is defying. Why, And this angle here is obviously not 20 degrees. This was my 20 degree angle here. So just gotta do to complement here 70 degrees where I could use this angle appear if that makes you feel better. I'm just pick this one by not going to say D five X that is adjacent to that angle. So it is, uh, co sign, right. So I'm gonna say d co sign Uh huh uh, which is gonna be five times the co sign. And remember, I'm using that Complement their coast 70 1.71 meters. That should be relatively small. Looks pretty tiny. That d five wise would be a lot bigger. It in some D five qy is gonna be opposite of my angle. Feta something say D sign theater. We're five. Sign 70 and I'm gonna get a pretty high value 4.7 meters that the sense. Both are positive to the rate in up. So De five X is a 1.71 and d five. Why is 4.7? Okay, now we need to find my signal dx on my signal, D y. So the next job is to just tally up the lines and find but some of all values in the X component. So sigma d x even add them all up. And then I'm gonna do the same thing for wise. I'm gonna write that in. Now that I have my marker out, C d y equals what? Let's go ahead and do that. So six plus 3.46 minus five point 0.66 Don't forget that negative in there. Plus 1.71 I'm getting 5.51 for my overall X positive. Which means I finished to the right, which makes sense. I am to the rate of where he started. And then maybe the same thing for my wife will be clear. This out. Negative two plus negative. 5.6 executed. Just subtracted about it. Plus 11 plus 4.7 positive. I finished upward. That's cool. 8.4 meters. Awesome. My done. I must be right. Of course. I don't have Sigmund E. So I don't want to muck up everything here. Something just kind of re draw what I see here. But really, actually, I can do it up here. I'm gonna muck it up. Why not? This is my overall resulting vector right in green. And I'm only showing now. Doing ready so really pops up as No, no, no. You shouldn't be doing this at home right now. Don't write this in a home. But I'm gonna do a solid arrow here in a solid here are here. And just try to explain you I'm talking about. So these two red arrows represent Sigma de Lyon. Sigma de ice. This is the Nets. Why components? And this is the Nets X component, right? And that dash green is my iPod news. This is a 90 degree angle. We know DX. We know. Do I? We're gonna find d how we're gonna find D. Yeah, we're gonna use five d squared equals net. Are Sigma d X sauce? A sigma d squared equals signal d X squared plus Sigma d y squared or Sigma d is the radical of Sigma D X squared plus D. Why squared? I hate this red marker. I definitely need to replace this, uh, to be 5.51 square plus feet. 0.4 square. Hey, holes 5.51 squared plus beats point for squared. Don't forget to radical the whole house. Second square second answer equals 9.75 meters. Sweet. I'm not done yet, but I do want to. Compared to my math and my graph route, there's definitely sizeable difference here. I think if you do this at home, you're probably getting more accurate graphing than I did. You have a pretty fat markers, and it was a little haphazard. Uh, this is definitely the more accurate Now, you know, I did around a little bit. It's still completely significantly more accurate in this guy here with it. Obviously still very similar. Lastly, I need to find my angle. I could find either this angle here where this angle here, depending on how I want to report it, either it will be east of north or north of east. I'm gonna go ahead and find this angle here, X I just for some reason find comfort on proximity to the X axes. It could just be my training in life. I do not know on. So for that, um, I need to envision this sucker sliding over here and this sucker sliding down here because this y value is actually opposite of this angle fade on this X value is actually adjacent of this Anglophilia gonna do my fatal work here, and I'm going to say I have Opposite of justice is to be tan. There is often, by the way, Tan. So it's gonna be my opposite value. Which again is my net de y over my adjacent value, which is my net de eggs. If I switch this evaded d x over d y. I'd be finding this angle here, So as long as I report the final value, it's really not a big deal. So tan fade on the tractor. You go there anymore. Tan theta is Sigma d Y 804 over signal DXE 551 That's gonna be some awkward number 804 divided by 55 born or remote about 51 I was just gonna be some weird number. 1.459 that's not an angle, because that's Tanta. And it is going to the inverse tan of that. Somebody second tan. Second answer, and I'm gonna get but what about 55 point will say 55.6 around it. 56 degrees. Look at that. To six degrees. All right. Pretty cool. Yeah, this is this heavy is against You're not gonna do much more in this Indian class. A teacher that you have my challenge you a little bit more, but in terms of ah, standardized stuff, this is it. I hope this helps. I'm gonna move into project emotion. The next video. That's it. Thank you.