 First of all, I would say to you if you did okay on the take-home quiz in other words If I can't remember what version of the quiz that I gave you, but if you can handle a projectile Launched horizontally from a cliff like a number one and you would feel comfortable finding anything Range or if you knew the range working way backwards and finding the height or finding the final impact velocity If you are comfortable with number two Which is at an angle, but starting on the ground key ideas is You know at the top at maximum your v y is zero you also know coming back down your v y final is the same as your v y initial But negative if you were okay with this one here the airplane with the crosswind and I think I added a projectile. I gave you a different version of the quiz I'm pretty sure there should be a quiz here called 2011. Yeah, there it is I Think I also then finished the quiz by putting a projectile and a cliff on there At an angle if you're okay with those you're good for about 80% of what's going on Okay, so if you were also able to handle this thing, okay Then you're in pretty good shape already if you want to look at the review that I gave you That was this bad boy right here. I double-paged it, but this thing I'm gonna tell you which questions I really didn't like Okay So number one is a great idea. I'm sorry number three hot number one number three here great idea of If I'm launching from the ground at an angle what I can ask you maximum height How fast it'll be traveling how fast will it be traveling when it's at its maximum height What will the Y component of the velocity be? zero That means it's traveling zero No fact the reason it's only two marks Look at the marks when you're doing these by the way reasons only two marks is it's the horizontal component That's your speed for a split second at the very very top and it's due sideways East or west or whatever Number three is good. I like number four Five is good. Okay Number seven. So here's an example of a using principles of physics I said five using principles of physics right to explain question This one says if I was answering this number seven I would probably heck mr. Do it why don't you find number seven in your actual notes? That would be clever. Hey, why don't you put number seven that would be really smart mr. Do it if I was answering number seven as a using principles of physics right to explain question If I was if they give me a using principles of physics right to explain question First of all if I was trying to answer this I would say I better mention those I'm not talking if not if somewhere in my answer I don't mention horizontal and vertical velocity components then I haven't answered their question and They want me to explain the behavior Here's probably what I would do It's up to you or you can just watch I can print this for you when you're done by the way if you stick around till the end They're talking about velocity. I would say something like this Vx, what can you tell me about the horizontal velocity of a projectile? How does it behave? Oh? What can you tell me about the vertical velocity? Now because this is worth four marks. I'd be a little suspicious if I just wrote changing You know what? I would probably say Changing I would write that down and then I would say Decreases zero at top increases But negative And the reason I might give them that why else did they give me that drawing? Maybe they want to be there. That's probably how I'd answer it four marks. He's cake Okay Eventually there's gonna be one of these on every one of your tests and eventually they'll get a bit more complicated But by that time you'll be far better Ellen question. Is that on the answer key to this? Yeah Looks like this as a matter of fact This is online So what number was that five or something seven oh there there's there's what I mentioned for four marks Now they were only wanting the velocity components. I probably didn't need to say the acceleration ones But I did an extra information. That's correct. Can't hurt Okay Other questions that I like so I was on my which questions. Do I like rent? I like number nine. So specifically I Like you to be able to handle for some reason I forgot to copy the letter B But this is part B you should be able to handle Finding a velocity by finding two components and adding them together tip to tail and doing the Pythagoras and the graphs And if you need me to I'll do one like that in a few minutes or I'll do this one. Let's just keep going through here Hopefully the bonus video game that I gave you has helped you remember what the graphs do you have until the day of the test So you have until tomorrow morning to still complete the bonus video game once you've written the test I will no longer take the bonus video game Okay Question Nicole you look a little stunned there Last yeah, and by the way those last couple are way tougher than I give you right, but great Number 13 something like this I'm gonna give you either a river question like from last year or an airplane with a crosswind question They're both the same question instead of a crosswind think current instead of an airplane think boat But there's gonna be one written question where I'm gonna ask you to apply some vector math 16 and again is from the ground to the ground It's asking you to find the range and find the total time of flight totally fair game as far as I'm concerned Yes What what what I mean by I like it I'm telling you right now on the written section There's gonna be a from the ground to the ground. I won't tell you exactly what I'm gonna ask But you better be able to handle it and be able to find out whatever I'm asking How long in the air for what's the range? Oh, how what's the maximum height? Oh, how long to get to the top? What's the velocity in magnitude and direction after whatever whatever seconds? Okay? 17 Just asking you do you understand what change in means what's changing anything? Final minus initial a little bit of vector subtraction there I think 20 I just don't like as a diagram that looks yucky But I might ask you to add two vectors together and find the resultant like on your quiz I think I gave you a force in one direction a force in another direction. That's it. What's the net force, right? Um I've already mentioned this Okay, so 25 here's again horizontally from a cliff So I totally like this one this one It's giving you the height of the cliff and it's sorry ah Nice twist here instead of giving you the height of the cliff. They're giving you the range Which is way easier horizontally actually you get a much nicer equation You can solve for t you'll solve for t horizontally And I'll bet you part b is find the height of the cliff you'll solve for d y vertically Oh, yeah, there it is how high as a cliff that'd be a nice horizontal off the cliff question isn't it Uh 29 absolutely you'd better be able to find the vertical and horizontal components I don't know if I'll ask that as a specific question, but I guarantee you'll be doing that about eight or nine times Hey, I'm off Is it the same one? No, I put it in the trash last time Oh, sorry for those of you at home. We had a little moth there. So absolutely Absolutely, I'll get it later. Oh, it's all right there Sorry folks at home. Um, so once again gotta be able to do components almost in your sleep. Okay Uh, let's see. What else do I like here? Okay, here's a great example number 31 Here's an example off of a cliff at an angle Although this one's a bit easier. They gave you time t which means that you didn't have to pull out the quadratic equation to find time t But told you like this question fascinating The scholarship one That one's a little overboard although I'd expect my top like if you're trying to get 100 in this course You should certainly try that one. Look at my answer key and see if you can figure it out So you're gonna notice on my big reviews towards the end. All of a sudden it'll say Section or scholarship questions. I'll put two or three if you're going for the 100 in my course They're worth trying because if you get those you'll find the test to walk in the park. You'll be like, really? That's what they're there for No, the all you do when you hand this in I give you 20 out of 20 for doing all the questions You know where you get the bonus marks you do better on the test I'm really trying in grade 12 like even the video game bonus marks I was uncomfortable doing that until they dropped the provincials now that they've dropped the provincials or made them optional Then I'll give you a couple of bonus marks. I want you in grade 12 to get used to doing things for the sake of Getting better at it. So you'll do better on the tests because in university Nicole that's where your grades gonna come from right and I'm assuming most you plan on going there next year or the year after I will say this though. I like number 35. I like number 35 number 35 That's a nice question. Okay So having said that Anything that you would like me to go over specifically and I'm freezing on this one Anticipating that maybe people would like me to do number 35, but I don't know. Yes Have you looked at my online solution key yet to try to figure it out for yourself? Okay, I'm gonna say I will I'm willing to but if you look at my online solution key and try and figure it out guys Can you whisper? I feel like I'm gonna talk over to you If you look at my online solution key and try and figure it out for yourself You will have learned it better. What I'm gonna do is do one very similar to this. Okay 25 40 35 degrees. Okay, so I'm gonna do Something like this Quick that wasn't where I wanted the screen flipping to go. Let's try that again Undo Click right there click Okay, this time put it somewhere nice like right down there. That's better so If you want to you can quickly sketch this on a scrap piece of paper or you can just watch and I'll print this up for you At the end. I'm gonna make the initial velocity 31 I'm gonna make the angle 32 degrees and I'm gonna make this distance here 42 Now the only risk is Brennan, Brennan, I'm not sure whether it's going to be on its way down when it hits the wall Or on its way up when it hits the wall So I may have botched the diagram by changing those numbers But we'll be able to tell whether it's on its way down or not depending on what we get for vy If vy is negative we'll know it's on its way down vy's positive will know it's on its way up Okay, so same question different numbers and that way you can still try that one there With what velocity magnitude and direction does the projectile hit the wall? I'm gonna just for the drawing And I'm gonna assume it's on its way down. I'm gonna assume the velocity is like that. That's what it hits the wall at What that really means to me Brennan is that I can break that velocity up into Vx which never changes And the final velocity vertically just before impact which is going to be changing the whole time In fact, you know what this question is really asking me to find vy final. That's what I'm going to spend the most time on Give me so far Are we being launched at an angle? components Vx is going to be 31 Cosine 32. Are you okay if I go that fast? and vy Is going to be 31 sign 32. Can somebody crunch those for me, please and actually give me your numbers I don't know what they are Don't I'll rush for your calculators at once or anything? Yeah 26.3 Okay, give me one second. I'm gonna write that down. Sorry. I'm just moping down some lunch meat that I didn't get to That was a little disgusting. Sorry. What's vx? vx is 26.3 Give me one more decimal place What's vy to four sig figs? Because this isn't my final answer. So I'll carry if you have two sig figs if I can 16.4 Okay You okay with our approach so far Is it Brendon or Brendon? Brendon with an e Right, so I have been saying it right. Okay. I was trying to slur it for a bit. They're kind of a brand And because I couldn't quite remember So and you're okay with with Brendon, you're okay with this conclusion here of me saying look if they want the impact velocity I can't find it directly, but I can find the components and then I'll add them tip to tail like I've drawn All right Vx we just figured out That's nice. I'm still going to go Horizontal and vertical I'm still right away going to say horizontally the acceleration is zero vertically the acceleration is negative 9.8 And I'm going to say the horizontal velocity was 26.29 And the vertical initial velocity is 16.43 and with only two pieces of information in each column I can't do anything else Let's go back and look at our question. Is there something else that they told me What Alex? They told me dx the range. You said dx. Yeah the range So that which tells me I'm going to solve part of this horizontally now. I know that dx is 42 why does that help me because I can find t Which almost always unless they tell you the time of flight That's almost always in any projectile your first goal You want to find out how long it's in the air for and then it falls apart from there Can you tell me an equation that has those in it again? Bring your formula sheets tomorrow. I have a few spares, but I don't have 30 spares. Yep You ever got one? I'll get you those before you go Okay That you know what why don't I do that right now because that will help your learning right now Hey, can you tell me an equation that has a v d and t in it? In fact, I'm pretty sure that the half at squared will cancel because a is zero In fact, I'm pretty sure we're just going to get this Scroll down a bit. Mr. Dewick Scroll down a bit. Come here. I'm pretty sure we're just going to get this d equals v xt In fact, I think time is going to be the distance divided by the velocity. It's going to be 42 divided by 26.29 Is that okay lia? Yeah 42 divided by 26.29 Time of flight before impact Is 1.598 and I'll carry a few extra sig figs because this is not my final answer either 1.598, but now I know over here 1.598 Why does that help me? Do you remember what I said this question was really asking me to find? I said, you know what? I'm going to spend far more time trying to find This that's what we've been doing so far if I now right underneath here v y final Can I find v y final from that information? Yeah v y final is going to be v initial plus At it's going to be 16.43 Plus negative 9.8 times 1.598 Boy, this is going to be really close to a velocity of zero and I think it's going to be positive. Is it someone crunch it for me? They almost I almost inadvertently fluked into having a dead horizontal when I hit the wall, which would have been really boring Someone else want to double check not that I don't trust alex, but I don't trust alex 16.43 plus negative 9.8 times 1.598 Grace you all slow folks You get that 0.77385 That's using the full value of time. So I'll go with that 0.77386 Is that what you guys got? No. Yes. No Yes, or no 0.76 Yeah, but did I type I might have typed it in wrong? Okay, I'll carry this one positive or negative meant to be obvious positive or negative My diagram's wrong, right? Really it should be and if I you'll have lots of room I generally on the written put one question per page of an entire page to do one question Because I've tried to tell you do your diagrams big so you'll have lots of room I'm going to Redraw this because I can erase really really actually no because I want the viewers at home to see this I'm going to go. Nope. It's not that it's actually as it turns out this 26.29 Plus this Which is 0.77 386 Here's my impact velocity Trevor by the way, this is really a bad scale diagram if this was 26 long This is 0.7 long really it's your triangle and I won't draw it that way, but really your triangle should look like That which would make it really awkward to find the theta so we're exaggerating now just to make it easier But I should point that out Is that okay Brendan are you okay from here on if I said to you find the velocity could you do the Pythagoras? Could you do the trig? You're okay with that that that's your final answer your final answer would be now do the Pythagoras and then Trig it's going to be tangent and it would be in this case above the horizontal as opposed to below the horizontal For your direction Is that all right? So that'll let you try walking through number 35 on your own We did one like it in our notes as well in lesson seven I think Any others from the review or specific situations that you're like, yeah, I'm not so Hots about Yeah Sure. The extra review is not bonus. You're not getting marks for doing it You just you'll get extra marks because you'll do better on the test. Yeah What number by the way June 85 June 87. That's the provincial exam that I wrote I got that one right I graduated in 87 Sorry, which one Alex? Number 16 nice Here's a good example of an airplane kind of a question I have a feeling this one's going to be sign law Cosign law which they used to emphasize more because we were smarter back then they've eased up on you guys a little bit They haven't done as much sign law cosine law. They've waved out. So let's try this one together I did say there is going to be some kind of an airplane traveling or river Current question But I said I'm pretty sure on your test. I kept it a little better I think I kept it at a nice 90 degree angle What you do need to know for an airplane is this equation And it's not one that's on your formula sheet. It's common sense. It seems to me The velocity in the air Plus the velocity from the wind That's what gives you the velocity On the ground that's what Whatever the engine is pointing in plus whatever the crosswind is blowing at that's what the radar detects Okay, you see what I mean by that's kind of a common sense equation. I think that kind of hopefully that makes sense to you as well Oh, yeah Engines plus the wind that's what the ground sees now. What's this question asking me to find alex It wants me to find this How would I get this by itself alex? How would I move this over? Ah, we're going to end up subtracting vectors here. We're going to get velocity Of the plane in the air is going to be velocity on the ground Minus velocity from the wind alex. How do I subtract vectors? It's a trick question I don't I'm going to change my equation and look up. It really is that We don't subtract vectors. We add the opposite, right? Here's my equation Now i'm going to dump draw a little picture What's the ground velocity? Oh did they say directions? That was silly of me I should have put a compass rose on here a long time ago alex because god knows I've watched that many a time Ground velocity 65 degrees south of east Ground velocity There's east That's about 65 degrees South of east There's my ground velocity and how big is my ground velocity? 475 That's that part of the equation I'm going to add to it the opposite of the wind What's the wind what's but but's the wind what's the wind right now 45 direction East what's opposite What direction I'm going to add 45 to the west How am I going to add these two together draw them Tip to tail this is going to be a fairly challenging diagram This is going to be where your geometry 11 is going to come in really really really really handy With me so far though Joel we're good so far Okay Would you have said that no matter what? I figured so Joel how am I going to add these two vectors together draw them means it's going to look like this 475 plus And 45 would be pretty short compared to 475 Alex here's our resultant from the tip of the second one to the Hang on mr. Duick. I drew that backwards Here's our resultant from the tail of the first one to the tip of the second one Here is um, do you see a right angle here? It's not going to be so katoha It's going to be sine law cosine law, but do you see any angle in my drawing right now not yet Here's the only angle. They gave me Ready. I'm going to mark this up. Don't write this down How big is that angle Alex my friend? Let's do that again How big is that angle? Really you're going to make this vanish on me. Okay Sorry, something's vanishing that's 65 degree. Okay I Guess this dude. I'm using pen as pointer. I am this is 65 degrees right here. Can you see a zed? Okay Those will come in incredibly handy this year Absolutely, so Alex the real question is how big is that angle? 65 degrees That's the only angle you can't find we can't find that one because it's all yucky slanty In fact, you know what else I don't like about this? I don't think I did that diagram big enough there That's better Isn't that cool? Now what are you okay on the cosine law? Okay, you guys want me I can do the cosine law if you want me to or if you're yes, sure thing It's going to be v squared equals 475 squared plus 45 squared minus 2 475 45 cosine 65 It's on your formula sheet Brandon. See if you can spot it It's on the shrunk down part of the page. Yes, it's there somewhere. Okay So you don't have to memorize it you do have to be able to apply it And this is going to find you Alex v squared. So what do I remember to do when I'm done? No Just square root we don't plus or minus some physics because we're dealing with real life data So let's try this You get the velocity is 458 Kilometers per hour By the way, I misspoke you get the speed is 458. Yes. How do we turn that into a velocity? We need a direction And here's where this question is nasty and I'm going to go to my answer key The reason this one is nasty Really nasty is because unfortunately This side here isn't nice and vertical or horizontal I can't find this angle that will not help me find a direction What I'm going to do is I'm going to go and I'm going to find That angle right there that angle right there is east of south Okay problem Where the heck is that angle right there? Well Let's look at my answer key. I'll show you what I did Uh Old unit review answers. What number was this 16? I remember Doing this question years ago and going wow I was apparently pretty smart back in high school Okay, so I did the 65 65 I said that angle there theta I found it is 5.1. Oh And I know from my zed that that was 65 right there. So if I'm going to use this angle, I can use south of east 65 plus 5.1 and that's where The 70.1 came from 65 plus 5.1 So I'll say this again. Are you ready? I guarantee there's going to be a question like this on your test with some kind of an airplane crosswind thingy But I'll set the triangle up to be right angles. I'll make it artificial. I understand this is way more realistic Planes don't all fly at 90 degree angles to the wind But I'll it'll be a right angle track Okay, does that make sense any others So that was a great review of the Vector math portion How do they see you back there keep forgetting you're back there? You can you see okay? Okay Yeah You okay with south of east it's south of east it's heading That way right or you could also have gone 90 minus 70.1 you could have gone 19.9 degrees east of south if you had found that angle right there Which you can also find in a roundabout way Your other option alex for what it's worth would have been now that you've gotten this far Add a right angle if you find this These two add to 180 and once you know that you know that because that's 90 That's a lot of work Kara you have a question. Are you just stretching? I have an answer So specifically For a question like this when we're looking at it sideways Up is not north Right, I mean that's not north That's not south in real life So when you're looking at it sideways and we want to show That way Or that we can't say north or south instead. What we say is Above the horizontal, which is what this one would be here Or below the horizontal, which is what this one would have been if we had actually ended up heading downwards That's when we're looking at the side and projectiles. We are almost always looking at sideways Now what I said Kara was if you called up north, I wouldn't take marks off, but I think bad thoughts about you I'd probably put a little frowny face on the next to there on the test Maybe make a little frowny face try maybe But I wouldn't take marks off I double-checked that when I marked the provincials and they said, yeah We just kind of think though if they're silly for not really realizing that's not north If I got something in the marking session, the guy in charge That's not north Why are you giving the marks for that because we're nice You understand, right? That isn't north. That's uh Above the horizontal and that's below the horizontal Is that okay? Yes, yes any others Is that a handout? No Yeah, absolutely I'll make one up and I'll try and think of every possible thing that I could ask Okay, so Let's give it an angle of 38 degrees Let's give it an initial velocity of oh, let's put some speed on this thing 142 meters per second And let's suppose I told you the height because this is the toughest if they tell you the range Horizontally since a is zero everything's easier to solve for let's suppose. I gave you the height and I told you this cliff was 16 meters high What could I ask you I could ask you to find components, but I think you guys are all okay on that Okay, so let's assume that's a done deal What could I ask you one of the first questions I could ask you is Fine time are we at an angle? components So no matter what we're gonna have to do that anyways I would say vx and you said I was okay doing it this fast 142 cos 38 and vy was 142 sine 38 because you remember that vy is sine and that's your stupid way to remember it, right? So 142 sine 38 87.424 I figured that's good because there's a nine right there. So this is really close to a four That's a good place to round off to should be reasonably accurate 142 cos 38 Oh, this is nice 111.9 because that's a nine next to the eight and a seven next to the nine. That's pretty close So 111.9 By the way, can you tell me right now? I'm gonna be solving this horizontally or vertically and how do you know? I'm gonna be solving it vertically You know how I know Kara, you're right louder They gave me a vertical displacement a vertical distance Okay, so let's do our usual list Brett are you making fun of me? You were weren't you? Yes, but I have to otherwise I can't talk see if I don't do that you guys can't see pause Let's keep going. Oh and Brett I would automatically write this as well vx and vy initial vx is 111.9 vy initial was 87.424 And Kara you pointed out that I know dy what's dy careful Yes By the way, if you miss that you'll either get an error when you're doing the quadratic formula Or you might sometimes it all depends on the values that I pick You could get solutions that are completely nonsense And I'm gonna find t from here Now you guys like to use the quadratic formula or do you guys find v final and then use that to find t? You know what we're going to do that anyways because part c I'm going to ask you to find impact velocity in which case you'd need to know vy final anyways So let's find vy final vy final Is going to be vy initial plus at It's going to be 87.424 plus Negative nine point it hang on mr. Duk Try that again I can't I don't know t I can't use that one yet vy final squared is going to be vy initial squared Plus 2ad this one works because I know vi. I know a I know d I'll remember to take the square root when I'm done and here alex I will remember that the final velocity is negative because just more hits the ground. I'm pretty sure it's going downwards Okay It's going to be 87.424 squared plus 2 times negative 9.8 Times negative 16 87.424 squared Plus 2 times negative 9.8 times negative 16 square root I get a vy final of 89.2 But it's heading downwards negative negative Does that seem right to me 16 meters only 2 meters that well 16 meters isn't that high I haven't made a dumb math mistake have I I don't think I have Plus 2ad D It's vectors. It's vectors. It's vectors Yeah, I think I'm right Now that I know vy final now I can find t T is going to be vf minus vi Over a it's going to be negative 89.2 minus 87.424 all over negative 9.8 time equals Negative 89.2 minus 87.424 All divided by negative 9.8 brackets around the top And I get a time of flight of 18 Well, you know what since they want this as an answer. I'll go to two or three sig figs I'm going to say 18.0 up here I'll go 18.02 here Seconds units make sure in your final answers make sure before you hand in your test you always check for units And sig figs in your final answers So one of the things I can ask you from a cliff this time Okay, really quickly. I'm just going to cheat and check it on my quadratic solver to make sure I get the same answer doing So it's a quadratic I'm just a little suspicious why this velocity is so close to the initial But I'm just thinking maybe 16 meters isn't that big a height. It can't speed up very much in that short of time I don't know so bear with me for a moment can be d equals vi t because I have a t squared so No second function quit app Those of you at home bear with me Fully smoked. Yes, finally a root finder degree two. A is going to be negative 4.9 b is going to be 87.424 And c is going to be it's negative 16 on this side when I move it over it's positive 16 so Positive I don't put a plus sign there dick so 18.02 whoo, I am right Good b find the range Well the range is dx And it's equal to that You start drooling soon there kiddo Your head's turned over about a 45 the mouth actually started to drop open and you tried to close it And it just started dropping open right away I was waiting for one of your eyes to go down and one of your eyes to go up or something like that You're gonna make it Or I shall yell again if I need to I could shock you with the fly swatter Those hurt. Have you played with those at all? Then get your attention Brandon you okay with that? But I'm the range Equals whatever I could ask you to find max height If I say the word height Vertical or horizontal Okay, what do you know about the very very top of any projectile? We still know that a y is negative 9.8. We still know that v y initial is 87.424 87.424 But I know one more key piece of information that they're very very top vertically what? What's zero and that lets me solve for d fairly conveniently Vf squared it's gonna be that one So I think d is gonna be vf squared minus vi squared all over 2a It's gonna be zero minus 87.424 Squared all over 2 times negative 9.8 Now that'll tell you how high you go above the cliff To get the actual height since the clip itself is 16 meters high I'll add 16 to my final answer and that'll tell me how high above the ground 300 make sure I type that in right zero minus that squared all over 2 times negative 9.8 389.9 390 Meters above the cliff plus the original 16 meters I can add 16 in my head on a test. I'll use my calculator just to make sure I don't do a dumbest rake 406 meters is its maximum height. How long is it in the air for? Okay, so here would be an example of what I would consider an a minus level question d find v after 15 seconds At time 15 seconds, what's its velocity? Oh That says speed what's its velocity magnitude and direction? Well, is it on its way up or on its way down? What was the total time of flight? 18 seconds so after 15 seconds you think it's on its way up or on its way down I'm pretty sure now if it's ground to ground. I know it's exactly half of the time going down and half the time going up This is a cliff but the cliff is 16 meters and we just figured out that it goes 390 meters into the sky I think it's almost halfway. Anyway, I'm positive. It's on its way down. I think what they're asking me to find is I think what they're asking me to find Is that That's v What else do I know? What would you do with this to try and find it? Because I like this question. I like this question Ah, I would do this right away alex absolutely and I know vx. Don't I what was vx? I scrolled down I wrote it down way way back here 111 point 111.9 111.9 and vy is uh Now the most common mistake kids go. Oh, it's 87.424. It's not that's your initial vy But it's amazing how many kids do the pythagoras and you know what they get for their answer when they do the pythagoras? They get exactly 142 Because they're just uncomponenting without realizing it and you know what they get for their angle trevor Would you believe they get 38 degrees and they're not clever enough to notice those are the same numbers that I gave you So don't be one of those I need to find vy Final at 15 seconds Well, I know time is 15. I know vy initial was 87 point. I erased it. That was done four two four four two four I know a y is negative 9.8 Could I find vy final? And could I then plug it in right there? And could you then do the pythagoras to find v and could you then find the theta and cara? This would be a theta below the horizontal for your direction Okay, that would be a nice question nice twist instead of saying when it hits the ground Tell you how far along it's gone and find the velocity at a specific point hanging midair Pretty kind of nice What if vy final ended up being positive? What would that tell me? That's still on its way up I don't think it is in this question. But if you didn't know the whole question Okay, give her an elbow. I'm gonna give her an elbow Okay, and would you like my little nerf baseball bat? I can loan you that if you It's therapeutic and helpful Okay, what else can I find from a cliff? Well, it's the same question as in d But party find the velocity when it hits the ground the impact velocity Which would look like that vx would still be the same you'd find vy final when it hit the ground And you could either use t or a distance of negative 16 meters to find vy final and again pythagoras And again, uh, I think shift tangent is what most of the angles have been in this unit. I think that's it for off the cliff Don't think I can ask Anything else Okay, that was a great question Any others You know what I would do best way to study Do the review You'll have seen about 85 percent of the questions Read through the extra review that I emailed you guys and any question that you go because a lot of them Will be familiar by this point. You'll be going. Oh, yeah, I just did that with different numbers I just did that with different numbers anyone that seems unfamiliar Glance at my answer key that I gave you look at it. Oh, yeah, that's what I would do Then you're fine if you're still a bit Try it With my answer key in front of you and see if you can puzzle your way through it If you do that As far as I know, there's only one curve ball I'm specific multiple choice question Any other questions otherwise, I'll end but if there's any other questions, I'll still go Who would like a copy of these this print out here? Raise your hand if you want to copy one two three four five six seven Yes, I can solve it Can I take shortcuts? So the Pythagoras I would go like this. Well, first of all v final v final is going to be v initial plus a See it times t 15 because that's the time they gave me A v final is going to be negative 59.576 Which would go there so it's going to be 59.576 squared plus 111.9 squared Pythagoras says take the square root of that the magnitude would be 127 points That's 126.7 be 127 would be your magnitude meters per second at The angle would be a shift tan and it would be Shift tan of 59.576 over 111.9 the angle ends up being 28 degrees I'll print this up for you. Hang on Oh below the horizontal Is that okay? So seven copies you guys want? Okay, let me just pause the recording