 We're good number three Car travels 15 meter second. I'm pretty sure vi is 15 they want me to find a They've given me T and they've told me the displacement is 85 meters Is that okay, Caitlyn? I'm looking for an equation that has those in it. I think it's this one I'm gonna solve for a now. This is an awkward equation to get the a by itself, but it can be done It's not as bad as all that I would minus the vi t over you could plug the numbers in ahead of time on this one If you really wanted to but I'll get the a by itself. I would minus the vi t over and I would get this well it equals a T squared over two because I prefer it over two than a half in front and This is also one big fraction The two would move To the top and I'd have to put it in brackets because it's two times everything so far so good Sorry, no. Oh, yeah, and T squared would move to the bottom That should get you there. I hope so D minus vi t times two divided by T squared. Oh Let's find out to bracket D85 minus vi times t divided by T squared Is the answer point eight? There you go You know what we don't very often use this equation to find an acceleration Work number eight was requested number eight We kind of got to visualize what's going on and I'm almost wondering now if there was something I was not happy with the number eight, but I'm trying to remember Number eight says a child slides down a playground slide Accelerating from rest. I would probably underline the concept here from rest Reminding myself. I think vi is zero. By the way, who has number eight It's gonna have two parts while you're sliding and then while you're stopping Okay Traveling six meters and four point five seconds because I think what I need to do first is find out how fast They were going when they hit the ground. I think first in number eight. I need to find the final and It's gonna be V final squared equals. Oh, no, they gave me time. Oh, let's see what they gave me I want to find V final. I know the initial is zero. I know D is six I know T is four point five How can I use that to find the V final? Haven't I got have I got an equation that has Vi D At and V final in it. Well, no, not blatantly However, I think I can use these three here To find Acceleration if I need to I think very similar strangely enough to what I just did with Caitlyn I think I have V T D I think I can use this to find the acceleration and once I find the acceleration I can find the final pretty easily I'm pretty sure we just finished saying with Caitlyn that the acceleration was equal to 2 D minus Vi T all over T squared. I think that's what we said. I'm going from memory here Actually, that's a lie. I just rederived. I just hit the equation in my head again because I can do that to my head 4.5. Oh, hang on. No D is six six Mine times minus. Oh, this is actually even easier than that because mr. Deweyck this we have done before Vi is zero. So this is all gonna vanish Vi T is gonna go away. This is just gonna be simply two times D divided by T squared I can do lots with this So the acceleration that I get here is Two times six divided by four point five squared You know what I'm gonna go point five nine two six because this is not my final answer I'll carry a few extra sig figs and there's a lovely nine right there. So point five nine two six I'll call it that point five nine two six Which means the final when you hit the ground and I'm running out of room here But I think I can go V final equals the initial plus a TV initial was zero. I think now I can go Acceleration times four point five and I get a V final of two point six repeating I'm gonna go two point six six seven because this is not my final answer either Two point six six seven meters per second. That's what I hit the ground at Now we're hitting the ground When I hit the ground, what's my final velocity when I hit the ground? What's my initial this? What else did it tell me The distance that my legs travel is point two meters not twenty seven point two meters So I think I can do some work here. Let's see in number eight then I can say The final is zero the initial was the final at the bottom of the slide Which is the initial when I hit the ground is going to be two point six six seven a I don't know D equals point two Yes, and now I can oh Oh a Equals vf squared minus vi squared all over 2d. I'm pretty sure where yay vf is zero I'll get a negative acceleration, which is good because I am slowing down I'll get zero minus two point six six seven squared all divided by two times point two Bracket zero minus I'm going to use this value since it stored on my calculator instead of two point six six seven squared I'll use that squared divided by two times point two Lay it on me Andrew. Tell me the answer is eight point nine is the answer eight point nine eight point four Sorry Oh, I put a point four up there like a complete meat head Because I did the math in my head I can fix that I think let's see by putting a point four there I've added it is the ants is the answer that Yeah Sorry, I accidentally stuck an extra two in the bottom trying to do some arithmetic in my head forgetting that Yes, 17.7, and I guess they dropped the negative. They were just interested in the magnitude Okay Almost two G's Not quite yeah, that's about right. I think When you go down a slide you have to flex your legs and then otherwise if you keep your knees stiff it hurts I think that 20 centimeters though Brett is low from what I recall when I hit the bottom of slide Because 20 centimeters is about what that I think my knees bent more than that when I was a kid. I Don't know it's been a while Emily's going why no just yesterday. I would oh never mind nothing. I don't still play out playgrounds Any other questions I would consider that kind of a question Fair game, but it's not going to be number one on a test But towards the end. Yeah, that's good thinking. I like those and it's also I'm going to make the assumption all of you have been on a slide. So it's yay applied physics that I experienced By the way, this isn't totally accurate because what do most slides have at the bottom? They level off to prevent this Right, they have a little jog at the end where suddenly instead of being steep it levels off for about a foot and a half But but that long it's all it needs, right? But there are some Older slides and you may see them in older playgrounds often They're big wide slides and it's a straight straight down and you better stop yourself. Those are great Also fun to run up Okay, then today And you want your uh calculators out and probably in degrees introduction to vectors In physics any quantity is either a scalar or a vector Scalers have magnitude only Vectors have both magnitude And you with me right Did I miss your group? Let's try that again All right, let's continue so Vectors have both magnitude and direction which is we're going to be looking a lot at vectors this year Specifically this year We're going to start going two dimensional much more than we did in physics last year Last year most of your physics was negative To the left positive is to the right this year we're going to have things going off at angles Some quantities vector quantities displacement For example 6.5 kilometers west The scalar equivalent of displacement is a distance 205 centimeters Velocity is a vector for example Eight meters per second East Sorry for this knees on line there Speed is the scalar Eight meters per second Just making up examples Acceleration 9.8 meters per second squared down often we would just put a negative there Then I left a blank here, but I said my example is 22 seconds. What's the scalar? I want you to put here Time Time does not have direction But I saw this sci-fi film one time where they were moving backward time does not have direction, but I know moves forward At least in physics 12 Momentum so momentum How about 5.1? Didn't remember the units for momentum Whoo, you get a candy later on Kilogram meters per second because it was mass times velocity Let's add a direction. I've already done a couple of compass directions Another way that we can sometimes show a direction is to put a negative that usually means in the opposite direction that we started Not always you could have a scalar that's being that gives you a negative answer as well All that means is you lost Whatever amount you're talking about So if you get negative energy, for example, it means you lost that much energy It doesn't mean that the energy was going backwards Volume is a scalar 1.6 cubic meters force is a vector 12 Newtons at 30 degrees south of east 12 newtons at 30 degrees south of east And then work or energy is a scalar 91 Joules Jay Almost always this year when I introduce a new topic or a new concept to you one of the first things I'll give you is the units the abbreviation and scalar or vector We can add scalars like normal math. For example 6 kilograms and 8 kilograms is 14 kilograms We can't add vectors like normal math to add vectors. We have to add them Vectorially, we often have to draw a picture. We have to dope That was an acronym. I gave them yesterday. Jeanette Dalt stands for draw a little picture. Sorry Watch the lesson if you're playing How do we add vectors? There's two ways to do it One stupid and long and one clever the stupid and long way is this when we we represent vectors with arrows One way of adding the vectors would be to carefully draw them to scale using graph paper a ruler and a protractor And then carefully measure the distance between them and that would be the answer that you got when you added them together I don't want to do that Better we could use tree Oh, but by the way vectors are either written in bold font So in a textbook you'll see a vector written in bold font But to hand write handwriting bold font Emily doesn't show up exactly you can try coloring it in really whatever So the other notation is we put an arrow above the vector Except over the years we've gotten very very lazy Years and years ago. It was that but we've gotten so lazy now We just kind of put a half arrow we clue in now. It's a vector That's a vector If you just want the magnitude of a vector Believe it or not that symbolized by that symbol. Hey math 12 humans. What does that symbol mean? It's actually yet the absolute value in physics means who cares about the direction lose the negative Just tell me the magnitude which really is where absolute value comes in handy So john travels five kilometers west And then eight kilometers north What is his resulting displacement? We could get out graph paper and a scale diagram Eh, we can use trig Let's try example one here. Oh, I should read what's inside the I almost missed the punch line that box It's bold. It's big. So I'm going to raise my voice ret says this To add two vectors. We draw them tip to tail. How do we draw them Mitch? Tip to tail. Thank you. You're with me now. How do we draw them Mitch? Brett, how do we draw vectors add them? Connor, how do we draw vectors add them? Fairly sure I did this last year too with my students. It's very very key Ah, but then there's one more thing you have to remember once you've added them tip to tail The answer the resultant is from the tail of the first to the tip of the second Let's try example one here. So in example one, we have five kilometers west and eight kilometers north They're talking about direction. I always draw a compass rose whenever they start talking about direction And we're saying we want to add this five kilometers west Eight kilometers north was west and north wasn't it? Yes And you'll notice Trevor that I've drawn it Roughly to scale. I tried to make the bigger one bigger and the smaller one smaller And eights almost twice as big as five, but not quite. I drew my It's helpful to roughly draw these to scale Sometimes you just won't be able to because the diagram will be too complicated Equals This is an equation. Now. This is a bit of a weird equation. There is a plus sign We've done that for ages, but we're adding pictures. Well, we're adding vectors. This is vector math Joel, how do I add two vectors together draw them? The tail is right. You make it okay. Sure. It's a little Sorry, you're good. I don't need to bring up the Tarzan yell or anything like that. Oh good stuff What do I mean by draw them tip to tail? Well There's the five There's the tip. So I'll put the tail of the second one Right there What's the resultant? From the tail of the first one To the tip of the second one This is the vector that all car call r for resultant Now there is a lovely right angle here. That's good Remember vectors have both magnitude and direction. First, let's find the magnitude How can I find how big r is? This is something I think we're introduced to you in grade eight It's a theorem It's Pythagoras. It's named after Pythagoras. He almost certainly did not discover it for some reason. It's named after him And if you can do Pythagoras on your calculator showing no work whatsoever I'm totally good with that except I've never went on a test in our notes We'll write it out just so that when you're studying, you know what that has me in so It's going to be eight squared plus five squared equals r squared eight squared plus five squared Square root of 89 9.43. That's two or three sig figs Units Is it kilometers? Is that what it was? Now that's the magnitude. That's the scalar portion of your answer, but we also want a direction So we're going to add An at symbol like in your email address What direction is this guy traveling? It's pointing In this direction here in fact, I'm going to argue that the direction is That it's This angle theta We did review how to find an angle a couple of days ago. Is there a right angle in this triangle conor? Then I can use so katoha conor opposite adjacent to my pot news the eighth mr. Giles You're both conor g's too. That's going to be irritating Sorry I agree How about the nickel? What trig function? Toa toa sadly is not a trig function Toa is what you say when you kick your foot against something you say I stuff my toa. Yeah, you know, we don't want that Tan yes, what you do on a beach. I agree What always goes next to the trig function? the angle Which I don't know it's going to be opposite over adjacent katie if you're showing work on a test This is what you would write. I would look for this To be able to give you part marks if you've got the wrong answer if you got the right answer I'm good with whatever you did, but I would say this theta equals math 12 What does that stupid little negative one mean? Yeah, that's how you write the inverse tan you may see some british textbooks Call that the arc tan And I've occasionally seen a calculator that calls it arc sine arc cos and arc tan right above it Is that another fancy fancy word for the inverse of the tangent or this cosine or the sine but a little negative one is easier to write What's the angle? How big let me make sure I'm in degrees. I am Inverse tan of eight over five 58 degrees 58 degrees what of what? North or south east of west what of what well, we would say this See how I drew this arrow here. I started out going west And then I made the arrow go in which direction of west This is north of west vectors Example two So that's how I can add two vectors together when they're lovely right angles I think example two is also a lovely right angle So I'm going to try to say try example two on your own here really quickly. I'm going to freeze my screen And let's see if we get the same answer with my screen frozen. Let's try that again. I'm going to freeze my screen there Now it's frozen How do I add two vectors together emily draw them? Well go for it. Let's try it Sort of yeah You'll notice brian I showed a lot less work than on the previous example This is really what I would consider fairly bare minimum I don't care if you can do pipe agris in your head great And then I went straight. I knew I wanted to find inverse to find an angle anyways So I said the angle is going to be the inverse of tangent and I put opposite over adjacent right there I didn't actually bother doing this line first And I got 31 degrees south of east Now there's a second possibility For all vector questions. There's almost always two possible answers In this question here, I drew the five I drew the five first and then I drew the eight What if I drawn the eight north and then out of the five or in this question here I drew the 10 first and then I drew the six. What if I'd done them the other way around? What if I'd gone like this? six plus 10 what if I was trying to find that You'd get the same resultant of 11.7 But in this particular triangle Your angle would be That one there You would start out going south and then you've gone east It's still going to be opposite over adjacent tangent, but it's going to be Opposite over adjacent of 10 over six 59 degrees also works Or 59 degrees also works Except this is not south of east. What's this one here? This one here is start out going south and then go East of south Both of those Brett are acceptable answers I usually draw them in the order they give them to me because I figure that's what you guys will do And I'd like my work to look like yours whenever possible But I'll always take both answers on a test What are these two add to 90 if I go back to this question? Or what's 90 minus 58 in your heads, please Jacob or 32 degrees west of north that would be uh That angle right there, which is legitimate. It just all depends in the order that you're dropping I take both How many got that? Oh excellent If we add displacement vectors of length three and two meters, what's the maximum sum? What's the minimum sum you can get? And explain your answer I'm going to draw a line down the middle and I'm going to go max over here Min over here So if you have a vector of length of two vectors one length three meters one length two meters What's the biggest possible vector you can get? Caitlyn Convince me Okay, you know what for my because this is one of those using principles of physics right to explain questions I told you about yesterday. I think here. I'm not going to go all fancy. I'm going to draw some pictures. I would go like this Three plus Two both in the same direction doesn't have to be both positive both in the same direction Equals Five great What's the minimum vector I could possibly get if I add vector three plus vector two Minimum vector I can get adding these two together Anyway Mitch is that hand up? Oh, yeah. No, that was actually behind the sink wave investment. Yeah, sure one convince me You're right. Oh So if I go three plus Two you're saying if I go three right and two left I end up with a One sure That's a perfect explanation for my esl students Almost no english. I wrote max and min I guess but you'll notice no english there The reason I say that often my esl students start to leave those questions blank I'll make you cry. You have to try no leaving questions blank Trend page For the three vectors below draw the sum two a plus b Plus point five c Hmm Nicole, how do we add two vectors together? Tip to tail. How do we multiply a vector by a constant? What is two a? You know what it is. It's the original a except how long is it compared to the original a two a is Twice as long Multiplying a vector by a constant That coefficient easy so it would look like this That's a There's two a roughly plus Then they want me to add b Plus Point five c. I think that would be c but half as long about that ish How do I add three vectors together? Well, if they actually wanted me to calculate numbers You really can't you really want to add the first two get an answer and then add the third one But have they given me any numbers on any of these vectors? Do I actually know any of the links? I think they just want the picture. I'm going to draw them tip to tail tip to tail tip to tail. I think it would look like this two a plus b Plus point five c I think there's my resultant in red From the tail of the first to the tip of the last vector It's just doing the trig here would be a little awkward Did we ever be asked to add three vectors? Uh, I can think of one later on in the year sort of but I don't do it that way I add the first two get an answer and then add in the third one And often two of them will cancel out quite nicely if you set it up just right We can also do vector arithmetic with our equations. So it says this An object is initially moving at three meters per second east. Did we all just turn the page? Then I'm drawing a compass north east south west So it's initially moving at three meters per second east It accelerates south At 1.5 meters per second for four seconds find the final velocity by adding vf equals vi plus at Now that's the equation that we know and love but now we're going to do it Vectorially I did this one with my physics 11's last year. I think I stuck this in What's it going to look like? Well, you know, I'm going to do here dull What a dull stand for a connor Yeah, you're going to make it because I kind of sense and you're starting to do Was I was I was I reading your body language right there or were you with me? Oh you were with me? I apologize then Drawing a little picture vi um, I think like that Plus What direction is my acceleration? South how big well, it's going to be a times t. It's going to be a times t It's going to be 1.5 times four Which I think is six, isn't it? 15 times four is 60 because it's 15 minute 15 Four minutes in it like 15 quarters in an hour. Is it six? So i'm going to draw a vector south How long is it going to be compared to this one? That's three long twice About there That's vi plus at can you see vf is going to be my resultant. Let's draw my triangle here How do I add two vectors draw them tip To tail V final this time is going to be that bad boy So this is the first time probably that i've given you a velocity in one direction and an acceleration perpendicular to it But i'm going to argue it's actually emily exactly what we did last year Same equation except just doing it victorially good solve it Quickly as fast as you can take shortcuts Cool. Let's keep going Let's kick it up a notch So I got a 6.71 meters per second at 63 degrees south of east or that would also be 27 degrees east of south Example three an airplane has an air velocity or engine velocity Of 200 meters per second north. So if the air is still that's how fast the planes engines can push it However, there is a wind blowing of 60 meters per second at 35 degrees south of east If I combine those two velocities, what's the plane's ground velocity or velocity relative to the ground Don't write this down here. Oh I'm going to draw a compass because I've turned the page Write that down Here's I think what we're talking about though. Don't write this part down There's my airplane pointing to the north right there The wind is blowing south of east the wind is blowing in this direction. So I think you would Try that again. Mr. Dewick There's my lasso a little button there lasso I think what you would see is the plane traveling kind of sideways Because the wind is pushing it towards the south and towards the east But the engines are pushing it north on the ground the radar would see it kind of going that way I don't think quite at that big an angle But get get the idea And I just wanted to move that around too. That's kind of cool airplane come Dulp Kara, what's belt stand for? I'm going to draw a little picture. Here's what it's here's my hint I gave you you want to think the engine velocity plus the wind is what gives you the ground velocity What's the engine velocity according to this question? 200 plus What's the wind yuck? Well Kara, what is that last little phrase right there say? Even after the 35 degrees I want that little the letter. Yeah Say it louder. You're right To draw that I go east first with a dotted line And then I draw an arrow south of east Does that make sense? There's the vector. How big is this angle right here Kara? Yep there How long is this vector? 60 My scale is garbage because 60 is almost well. It is three times shorter than 200. So I'm going to go like that This is how you cheat and do kind of to scale afterward I want to add those two vectors How? How do I add two vectors draw them? Hit the tail I'm going to get this 200 plus 60 the resultant is From the tail of the first to the tip of the second that puppy there Mitchell. Yeah. No, yeah Question for you. Is there a right angle in there anywhere? So there's going to be sign law coast sign law, but we've got a bit more information We can add because I still haven't figured out how that 35 degrees is going to help me. Well, if I look right here I'm going to mark up my diagram right now. I don't want you to In fact, I have something to let me turn this marking on and off Kara, I think this is the angle that you said was 35. Yes See it see it see it see it Um, if this angle here is 35, what do both of these angles here add to? Ah 90 so if this is 35 right here, how big is this one right here? Aha, I've got a triangle an angle in my triangle Often for non-right angle triangles, you're gonna have to extend a few lines Sometimes you will end up with this angle being in your triangle. Yay most of the time now So you told me this was 55 degrees And this is my resultant r Mitchell you already agreed. Is there a right angle? So now quickly go Do I have a pair where I know both the angle and the number across from it anywhere? Emily then is this sign law? Co-sign law This is the co-sign law. What's the co-sign law? Well, we wrote it as c-squared, but what letter do I have here? I'm gonna go r-squared equals a-squared plus b-squared minus 2ab Co-sign big r And if you don't remember the co-sign law it is on your formula sheet This is where it shines because really now this is reasonably plug-in chuggish ugly plug-in chuggish But plug-in chuggish r-squared is going to be what's little a oh heck 200 Squared plus 60 squared minus two times 200 times 60 co-sign of Pay five And I get planes velocity is 200 squared plus 60 squared minus two times 200 times 60 times the co-sign of 55 And I get it's going 29,834 Oh, I forgot to square root common mistake because I found r-squared square root 173 if I round off properly and that seems much more reasonable 173 meters per second Sadly It's not the answer. That's only the magnitude They wanted velocity they want magnitude and what? Direction Where's the direction so find the resultant where it starts And then find the nice line right next to it This black line here. What direction is it? Okay, so it's going to be of north What direction of north do I have to go to get to there? east of North so I'm going to leave a space for the actual angle itself, but I am going to write east of North because I'm also proud that I got that part And I'll put a little theta Right there. All right zay. Here we go right angle zay No Do I have a pair? I do now Because I now know are So now I can use the sign law to find an angle This is why I said you almost never have to use the cosine modified angle almost always once you've done the cosine law once You've got a pair What's the sign law going to be okay? It's going to be the sign of 55 divided by 172.73. I'll use this did 172.73. I'll use the noun round non rounded off more accurate value equals mystery sine theta divided by What side goes with mystery sine theta katie? More specific in this case Thank you katie is this one fraction equals one fraction I mean I can cross yeah cross multiply you'll get a decimal and then shift sign Theta is going to be the inverse sign of 60 times the sine of 55 divided by 172.73 So on my calculator, I'm going to go 60 times the sine of 55 divided by I still have my previous answer stored on my calculator, which is 172.72596 I'll take that one and be more accurate Oh Uh-oh I did inverse sine for some silly reason. Let's try that again And I get the sine of theta is 0.2845501 How do I find theta? inverse sine of this puppy And I get you get 16.5 degrees 16.5 degrees That's what the radar let's see A plane traveling at 173 meters per second Drifting 6.5 degrees east of north even though the plane itself is pointing to north the crosswind is moving You can do that question using components, which is probably how we taught you last year in physics 11 If you do that with components, which works it's about nine lines I'm going to argue the cosine law. You can master the cosine law much much much cleaner Significantly so Next page. It says this If you are uncomfortable with the cosine law approach You could use components This involves breaking every vector up into vx and vy If you want to use the component method Ask me later on in class and I'll show it to you I'm sensing most of you here were okay with the cosine law. I mean you got that. Okay Yes, I'm sensing most you were okay with the cosine law. It's a bit of number crunching Joe I realize that but it's mostly just typing So if you want me to do the component method with you, I will fill this page out with you later on I can also tell you kind of start your drill Brandon gonna make it Okay You get the same answer I prefer the tip-to-tail method, but you'll get full marks try the method Use the other one you like best turn the page Mr. Redmond, how do we add vectors together draw them? How do we subtract vectors? It's a trick question We don't We don't That's the short answer Instead we add the opposite if you want me to go a take vector a take away vector b What I'll do instead is going that's the same as vector a plus negative vector b where negative vector b Is vector b but with the arrow on the other end? There is Brett an actual method to subtract vectors and I learned it in college And then I found this and I went yeah, why would I teach them a separate rule when I don't need to? We can just keep using the same rule of how do we add vectors together tip-to-tail? Because you can change any subtraction question into an addition question for that the opposite So we're gonna do that A plane's ground velocity or velocity relative to the ground Is 240 meters due east? This is our last example If the wind is blowing at 80 meters per second due south, what's the plane's air velocity? Hmm Seems to mean the cold for any airplane out there The engine plus the wind gives you the ground speed or the radar speed Air or engine velocity Plus wind velocity Equals ground velocity What do they want me to find here? How would I get the air velocity by itself? minus that over We're gonna get this the velocity with respect to the air. That's what the engines are putting out Is equal to the velocity on the ground Minus the velocity of the wind We're subtracting vectors No, we're not because you know how I subtract vectors. I don't We are gonna add the opposite That right hand side is gonna be our equation. That's gonna carry help us to double What is the ground velocity? What's the radar measuring? Read the question Sean, what's the radar measuring? Direction I better draw compass because I've scrolled up So if I hear you This guy looks like this 240 Plus Sean, what's the wind velocity? How big? Direction, what's negative wind velocity then? direction Plus 80 That's going to give me my air speed That's gonna tell me How much the engines are putting out against that crosswind so that on the map I'm still able to go due east I guess this pilot is pointing his plane. I'll bet you he's pointing his plane this way So that when the wind is pushing himself it cancels out the this way portion and he ends up going due east How do I add these two vectors together Sean? Go ahead do it yourselves. I think this one will be a nice right angle And when all said and done, that's what I got Am I right? Brianna's nodding You know when you have the notes pretty good You got some game Or 72 degrees east of north would also work if we did the 80 plus the 240 So how do we subtract vectors? Well, have the opposite How do we add vectors from the tail? To the page Well, foxtrot comic I love foxtrot the guy who writes it bill amond Actually was doing his physics degree in university. He has a physics degree But also while in university he was doodling a lot and drawing a lot of comics. And so his friends said look Why don't you try getting these published? So he has a wonderful accurate nerdy math in the comics. I especially love the youngest boy jason who is an uber mega nerd It's great. So Peter the older brother is playing football with the younger brother jason. What pattern did I tell you to run? You said go 10 yards out then 10 yards to the right What pattern did you run? I went 10 root 2 yards at a 45 degree angle And are they the same thing if you had the vectors sure It's just football not math class. I think I rounded two decimal places. There's the first one The second one Jason's now the ball Okay, here's the play go 40 yards downfield then turn left and go 20 yards Then turn right and go 25 yards then turn right again and go 30 yards Then turn right and go 30 yards then turn left and go 10 yards Then turn left and go 15 yards then turn left and go 20 yards then turn left and go 50 yards And I'll hit you with the ball Peter's doing the math Won't I be right back where I started you can't throw very far Okay, here's the new play and it gets recorded back A couple of years ago. We actually ran this out in the field and you do end up right back where you started from It's raining yucky weather right now. So we're not going to it actually the math is accurate. I had to check It says homework vector addition worksheet actually first thing You get up the great big review that I gave you yesterday Jeanette, that's this bad boy here. This is due the day of the test The ultimate kinematics review. I gave it to you at the maniac class Sorry, I don't know yet. I'll always tell you a week ahead of time though But So you can't do every question on here yet. I told them which questions I covered You can now in theory do the following ones uh two four 13 15 17 24 I think that's it for now And I'm going to take a gamble here. I'm actually going to skip lesson four And give you homework from lesson four. So where it says lesson three homework vector addition worksheet I'm actually going to give you lesson four right now And I'm going to assign some quests from here taking the gamble that you remember some of this from last year and that'll give us So look up. I just gave you lesson four. This was going to be some more vectors This was going to be like the river question, but I think you all did it last year And uh, I will say this where it says handy hint change in anything is always final minus initial That's worth memorizing, but I'll flog that to death This is going to be your homework. So here are some questions you can try So I haven't reviewed finding components. I'm kind of hoping you remember But if not, I'll talk about it next class, but try number one Number two three is fine four is fine and eight is fine and I'm pretty sure You can scribble that out The answers are attached. I think yes. I hope I gave you the answers. Didn't I I think yeah So there's a few questions to try and then I have just a practice drawing your sheet for you