 Now, just a little note about this lesson six, technically it's due today, but if there is stuff that you did not understand, it is much more important that you figure out how to do it than hand it in, incomplete it. In other words, I'm not going to take marks off if you hand this in Monday or Wednesday. I'm going to be around today after school, tomorrow after school, Friday after school, et cetera, et cetera, et cetera. So I've had a request for question number three, I'll do three eight. And I think I can do it this way. I think I was clever, yes I was, so I can copy it. That was smart of me. You try it, Caitlin? Okay, first thing is, I'm not really going to use this 19.6. What I'm going to do first thing, because I notice it's at an angle, is I need to find the components, the components, the components, the components. So I will redraw this because it's really small. This is 19.6, there's VX, there's VY initial. Not a great drawing, it looks like VY isn't quite vertical, but I know it's supposed to be, so I'm just going to live with it. And this is going to be, what was the angle, 30 degrees right there. And Caitlin, I think you end up with VY being 19.6 times the sign of 30. Is that correct? Or are you okay with that? I'm skipping a couple of steps because I want to get an actual lesson done today. And I think VX ends up being 19.6 times the cosine of 30. And I think this ends up being 9.8, and I have no idea what VX ends up being. What did you get for VX? Nice and loud, sorry, 16.97, is that right, folks? Yep, people nodding. Now I've done the groundwork, I'm going to break this up into horizontal and vertical. I'm going to write down two things right away, horizontal acceleration is zero, vertical acceleration is negative 9.8, and I'm going to write down two more things. VX is 16.97, VY initial is 9.8. So far so good, Caitlin? I know one more thing, I know a distance, a displacement. Look carefully, did they give me a vertical displacement or a horizontal displacement in this question? They did, so what did you put for the vertical displacement? Oh, you did get the negative? You did get the negative? Excellent. It's very important to remember that the displacement is negative. Why is the displacement negative, John? Because you're ending up below from where you started, okay. It looks like I have three pieces of information under the vertical column, so now I'm going to tackle the rest of this vertically. What I really am trying to find is time of flight. And I said to you last day, if you want to, you can quadratic formula this by using D equals VIT plus a half AT squared. Or if you want to, you can find VY final at impact, remembering that it's going to be negative and then solve for T. Would you like to use the quadratic formula, method one, or would you like to use method two, okay? So if I find VY final, that's going to be VY final squared equals VY initial squared plus 2AD. That's going to be V final squared equals 9.8 squared plus 2 times negative 9.8 times negative 14.7. That's going to be 9.8 squared plus 2 times negative 9.8 times negative 14.7. Oh, missed the decimal. 8.7 squared VY final by a wonderful fluke happens to end up being the same as the angled velocity. That's just a fluke with the numbers. And John, that's also why your two errors canceled out this morning when you were doing it. As it turns out, VY final is 19.6, although that's not quite right. What direction am I traveling when I hit the ground, Caitlin? Negative 19.6. I don't like the fact that it flukes into the same, I'm worried you'll think, oh, that's the same as the angle velocity, no, we never use the angle velocity again once we find the components. It just happens with these numbers by a strange and a wonderful fluke, the angled component of the initial velocity just happens to be the speed vertically that hits the ground at 2. Is that okay? Now that I know VY final, I can find T. T is going to be VF minus VI all over A. That's going to be negative 19.6 minus 9.8 all over negative 9.8. And T works out evenly strangely enough, I think, to three seconds. Is that right? Is that okay so far? Now that I have time over here, I also know time of flight. It's three. And now I say, aha, I have three things. I can find any fourth thing that they want, a V, a D, or whatever, and this question wanted the range, which means they want me to find DX, which happens to be VXT plus a half AXT squared, VIT plus a half AT squared. But what was A? This whole thing is going to cancel. Yeah, the range is going to be 16.97 times three. 16.97 is really close to 17. 17 times three is 51, so I'm guessing the answer is just shy of 51, or it might even be 51 to two sig figs. 50.9, yeah, there you go. Is that okay? Do you see where you zigged? Ah, squared, yes, yeah. Range is horizontal distance, which is DX. Another word for range is horizontal distance, sorry. I know, in a projectile, that's why they call it a firing range. Like in a projectile, the range is range to target. I know, where do we get to math 12 when inverse and inverse don't mean the same thing as in physics? I know. Sorry, you're learning more things and you're realizing that knowledge gets splintered and not everyone uses the same terminology for everything. Okay, English is weird. We say fat chance will mean your chances are thin. No. Alright. Someone, not number 10, is that what I heard? Someone just got that. Oh, we do. I'm going to hold off on number 10 because I think I'm getting to it fairly similarly today. Okay? And I heard someone say number five. I'm going to hold off on number five because I'm going to be getting to that one today. Okay? Okay. So, as far as I'm going to be sending out an email update to you and your parents this weekend, it will not have lesson six on it. I'll probably type it in, but I won't activate it. Whittle away at this. This is physics 12. By the way, welcome to Two Dimensions. I think I said it at the beginning of the year, physics 12 was 11 done, but in Two Dimensions and Components. Okay? Let me hit pause. So, projectile motion, by the way, where it says kinematics lesson five, let's be clever and let's call it kinematics lesson six. I'll have to resave these and change the titles next year. And some of this is review. We said when we launch an object into the air, we'd call it a projectile. Projectiles travel in a parabolic trajectory, but it's easier to use vectors. By the way, there is something called vector mathematics, which lets you do these without components all in one fell swoop, but it's yucky. You'll probably end up doing it that way, those of you that take first year university physics next year, because in Three Dimensions doing components three times is a lot of work. So you'll try and find a way where you can do it all in one step. We break each projectile's velocity into vertical and horizontal components. Example one, right now, get your calculators out if you haven't already, break that velocity into its vertical and horizontal components. I'll freeze the screen. I'll do it up here. See if you get the same thing as me. And I get that. See if you get the same thing. Yes? Now, if I was using this to find more stuff, I would carry extra sig figs. But we've said this year if they ask you a question, give your final answer to two or three sig figs. So I gave that to three sig figs and I quit. But if they then said do something with it, either I'd have the number on my calculator and I'd use the longer decimal version. Or instead of typing VY, I might just later on in my calculator type 24 sine 36. And that way I'm not rounding off at all. And it's not that much extra typing. Summary of the changes, summary of what we want to know. So horizontal motion, VX is constant. The horizontal velocity is constant. This means that the horizontal acceleration is zero, which means that becomes that. This means that if you know the time of flight, you can find the horizontal distance, also Brett called the range of the projectile, I know. Or if you know the range, you can find the time of flight. Vertically, VY is changing, but AY is constant, negative 9.8 meters per second squared. D equals that. Couple of handy things. At the top of its arc, the vertical component is zero for a split second. That sometimes comes in handy. By the way, does this mean that the total velocity is zero at the top? If I throw something, ready Emily? Incoming. And back. At the top right there was the velocity zero. No, one component was, which component was zero at the top? Vertical was the horizontal component zero. So we can answer this question now, hopefully without me having to throw something in another person. Does this mean that the velocity is zero? I say to you, no. Because there's still a horizontal component. Other handy things. If you start from ground level and end at ground level, your initial vertical equals negative your final vertical. What goes up must come down, and it comes down at the same velocity. As long as it's the same height, same height. Ground to ground. Lastly, if you're starting from a vertical height like a cliff, the ground is below you, which means your final vertical displacement will be what, John? Negative. So, a projectile is launched from ground level at an initial velocity of 200 meters per second at an angle of 38 degrees. Dulp. Lea, dulp stands for draw a little picture. It's an acronym that I use. So whenever I say dulp, what I'm saying is let's draw something. There. 200. There's VX. There's VY. And the angle is 38 degrees. Good to see you back as well, sir. Good, find the X, find VY. This to me, I won't call it a no-brainer because you're having to trigger some thinking, but to me, this is as close as you'll get to three marks. I will, on your test, on at least one question, say, find the vertical and horizontal components. Hopefully you can do that almost in your sleep. Some of you, the way you're yawning, probably are doing it in your sleep. Not to mention any names. And do you get 158 meters and 123 meters per second or meters per second? Are my answers right? Oh, wow. I put them in brackets, but I was doing them in my head with no calculators, so there is a chance that some of these might be wrong. Sorry, doing them in my head is not showing any work, only on a calculator while watching TV. It wasn't the best way to make up an answer key. Now, Kara, you may have noticed often next to VY, I'll put a little I for initial. Why don't I put a little I for initial next to VX? Never changes, that'd be a waste of time. But VY does, so I might want to remind myself, this is what I'm starting out at vertically. And it's going to be getting smaller, smaller, smaller, smaller. Zero for a split second, getting bigger, bigger, bigger, bigger, but negative. Okay. Find the time of flight. Well, the first thing that we would do is we would break this up into horizontal and vertical. And you can abbreviate them H and V if you want to. You can abbreviate them Hori and Verdi, whatever, but something that's clear to you, in fact, I've seen some kids abbreviate it as X and Y, but to me, since we use the phrase horizontal and vertical, H and V would make more sense. And let's list our data right away. Let's defic. Lea, defic is another acronym. Defic stands for data formula insert crunch, and it's another approach that I use in physics as well. So I know AX is zero, AY is negative 9.8, I know that VX is 158, I know that VY initial is 123. How many pieces of information do I have under horizontal? Two. How many pieces of information do I have under vertical? I can't solve. There has to be something else, and there is. What else do I know? I know something else about vertical. Oh, what's my displacement? Ah, since I'm starting and ending up at the same height, I know that that's zero. How does that help me find T? Do I have an equation that has A, V, I, D, and T in it? I do. Which one? The quadratic, the squared, the T squared one. That's one. D equals VIT plus a half AT squared. If I plug in all my numbers, I get this. Zero equals 123T minus 4.9T squared. Mr. Duck, yes, Connor, where did the negative 4.9 come from? Where did the negative 4.9 come from? Half of 9.8. That one I've done so often, and I also know two times 9.8 is 19.6, because that shows up in the VF squared equals VI squared plus 2A. What kind of an equation is this? It's a quadratic. How do I know it's got a squared? How do I solve this one? I don't use the quadratic formula. I could. Am I wrong? If you've got your quadratic solver, knock yourself out. If this one factors, what's the first thing that I always, always, always, always, always, always, always, always, always, always, someone's got me always, always, always, someone's got me always look for when it says factor. You guys, I heard it. Always look for a GCF first. And if they didn't drum that into you in grade nine, well, then you never had me in math nine, and you didn't because I don't teach math nine right now. Always, always a GCF. First of all, because if there is a GCF, it almost always makes everything else smaller and easier to factor, and you'll catch the subtle one. There is a greatest common factor here. There is something that appears in both of those terms on the right. What? I heard it. What? You can factor out a T. Put your pencils down, look up. If I gave you this in grade nine, I'm sorry, in grade 11, zero equals 4x squared minus 5x. That's a quadratic. How do I know? It has a squared GCF. What's the GCF? You would have said, okay, factor out an x and it's 4x minus 5. What are the roots without doing any extra work? What are the roots? What did you learn last year as shortcuts? What did this give you as a root? I heard it. And what about here, Matt? It was change the sign of the constant divided by the coefficient. Change the sign divided by the coefficient. What if they had been really mean and if they had done this, 7x minus 3x squared? What kind of an equation is that? It's a quadratic. How do I know? It's got a squared. Yes? Factor out the x. You would say, oh, this is x bracket, 7 minus 3x. What are the roots? What's the first one? This is the easy one, zero. What about here? The rule is change the sign of the constant term divided by the coefficient. That's what you were doing with your shortcut here. It's just last year they almost always put the x first and then the constant term and so you probably didn't actually go through those steps. You just saw the root. But for what it's worth, it's change the sign of the constant term divided by the coefficient. Got it? Make sense? Take your pencils up. What are the roots? What's the root here? This is the easy one, zero. By the way, what we're saying is at time zero, you're at a height of zero. What's that really saying? The projectile was launched from around the, oh, mathematically that popped out, too. What's the second root? Louder, I think you're right. Change the sign, divide by the coefficient. Whatever the heck that is is a decimal, please. By the way, the reason I'm showing you that is if you're launching from the ground, it is still a quadratic but you don't need to use the quadratic formula and I think that's way faster, Jeanette, way faster. It is negative 123 divided by negative 4.9, someone? Equals 25.1 seconds, which is what I said. That's a unique situation where your quadratic will still stay a quadratic but not a yucky quadratic. If you're starting on ground, ending at ground. There are other ways you could have found the time of flight. You could have found the time to the top because at the top, how fast are you traveling at the top vertically? Zero and then doubled it to get back to the ground and you know what you would have got? 25.1. But you would have had to do two separate little solving of things and this got us there in one shift. Is that okay? D says, find the range. Okay. You know what another expression for the range is, Brett? That. Oh, by the way, what did we say the time of flight was? 25.1. I would walk over here where my horizontal section is and I would make a little note, hey, T was 25.1 and then I would smile because how many different quantities do I have on the horizontal side? Now? Three. Now I can solve for any fourth one. In this case, they want me to find the range, the horizontal range. I'm looking for an equation that has A, V, T, and D in it and it's our old favorite, our old stand by, our old reliable, D equals VX, T plus a half AX, T squared. And once again, woohoo! And I get 158 times 25.1, what do you get for the range? You get 3,960, almost four kilometers, sorry, 50, okay, so 3.96 times 10 to the third. If we go to three six things, E, find the maximum height, am I going to solve this vertically or horizontally? Am I going to solve this vertically or horizontally and there's an obvious answer screaming out of me in the way the question is phrased? Why vertically? Height, that's a vertical word, yep, okay. I still have my vertical stuff listed right here, except T is not going to be 25.1. Maximum height, the top, what else do I know at the top? I know one more nice thing at the top, VY final is zero. And they would like me to find DY, the height, the vertical displacement. And from up here, I know AY is negative 9.8 and I know that VY initial is 123. Do I have an equation that has VFDA and V initial in it? Which one, Mitchell? Did you say the letter T, because if you said the letter T, I don't see a letter T sitting anywhere here in part E, so I don't think I can use it. I'm looking for an equation that has VFDA and now, here's what Mitchell said. Why wouldn't you just take half of the T? Here's why, if I got that wrong and I take half of it, I guarantee I'm getting this one wrong too. That to me is bad test writing. I'll use what they give me whenever I can. Right now in here, the only one I've had to calculate is my component and I can do that in my sleep. I'm going to use the one equation that uses these without time, because that way I'm not using perhaps bad data to find a bad answer. Which one? Yeah. Can you get the D by itself, please? No. Why don't you forget to say out loud, VF squared minus VI squared, all over 2A, yes I'm yelling again, Joe. If you're scaring me, get used to it. Zero squared minus 123 squared, it was 123, right, yeah. All over 2 times negative 9.8. Caitlin, do I need to square root this one? This answer? Do I need to square root my final answer? No, just making sure that I dig that little, you know, put my thumb on that little bruiser. How many numbers are on top, Kara? In my fraction, how many numbers are on top? Two, rackets around the top, yes. How many numbers are on the bottom? Rackets around the bottom, yes. You want to practice these on your calculator. Every year there's somebody who gets all the answers wrong on their test, even though they've written things correctly, and I know they were too lazy to bother trying these on their calculator in class. Dumb. Do you get 772 meters? So far so good. Next page. Caitlin, look at part C of example two. That's the question, question five that you were asking me, basically. It's going to be the same idea, finding a final velocity if you know the time, okay. In fact, look at part C in example two. It's similar to the one in example 10, but in example 10, the question 10 that you asked me, instead of giving you the time and saying find the final velocity, they gave you a horizontal distance which you could use to find the time and then find the overall velocity. Trust me. A projectile, it says, is launched from a 45 meter high cliff at an angle of 64 degrees with the horizontal. And with an initial velocity of 36 meters per second. Dump. Let's draw a little picture. There's my cliff. There's my projectile, 36 with an angle of 64 degrees, and this height here is 45 meters. That's a pretty good picture. You'll notice I did it nice and big. I've learned to make dumbness strikes when I do small little midget pictures. What does part A want me to find? Range. Can't do it yet. In fact, you know what I need to do before I go further at all? Let's find the components. Let's do that right over here. I'll freeze the screen. Try it yourself. I went for sig figs because they didn't ask me to find the components, so it's not a final answer, so I'm going to keep some extra decimals. Poster, door, really, you've had a television all your life. It can't be that they get this reaction anymore. Your TV at home is never on? Well, talk to your parents. Maybe there's a reason for that. Now what would I do? Now what would I do? What did they ask me to find? Range. I can't find the range. You know why I can't find the range? To find the range, I have to find something else first. Time. You know what this question is really asking me to find, really asking me to find time of flight. How am I going to do that? Oh, let's break our page up. Yo, let's break our page up. By the way, 15.78, I've got to get this battery replaced. It's barely ever working. Sorry. Thanks for letting me know. I got a VX of 15.78, a VY of 32.36, and I broke it up into components, and right away did my horizontal vertical. It would be nice. An easy question, Sean, would be if they'd given me the time of flight, then they could ask me to find the height and the range, and I could find those both pretty easily because they're both distances and more plug and chug. But here, they've asked me to find the range. Oh, I know one more thing, by the way, because right now, I only have two quantities in each column. I can't solve for anything. What else do I know? Vertical displacement is negative 45. And since I have three things here now, I can solve for t. You can either solve for t using the quadratic formula and your quadratic solver, and I'm good with that, using d equals Vi t plus a hat of t squared. Or you can find VY final, negative when it hits the ground, and use that to find time. Who would like to use the quadratic formula approach? Who would like to use the VY final approach? Well, the vote was apparently five to two. Thank you for participating. Okay. VY final squared equals VY initial squared plus 2ad. VY final squared equals 32.36 squared plus 2 times negative 9.8 times negative 45. And Caitlin, what will I do at the very, very end? I will square root. And I get 43.9. Which is actually wrong? Kara, what did you say? I think, did you say negative? Yeah, I was reading your lips. And the second time when I said what you say and you didn't say it any louder, it's still reading your lips. Yeah. Turns out, VY final is negative 43.92. So I have VY final, VY initial, a, I can find t. What equation has VF, VI, A and T in it? By the way, I'll say this again. If you haven't clued in that it's really helpful in physics 12 to have your formula sheet out in front of you during the lesson, which is why I gave you two of them in the first place. You might want to actually clue that in because I'm also wanting you to train your eyes to look in the right place. That helps, believe it or not. At least one per table would be clever. So which equation? And I love the fact that you got the t by itself. T equals VF minus VI over A, which is going to be negative 43.92 minus 32.36 divided by negative 9.8 bracket, negative 43.92 minus 32.36 closed bracket divided by negative 9.8, 0.8. I get a time of flight of 7.78 seconds. Someone else want to double check me? Quadratic guys, if you use your quadratic solver, you should got a negative answer and then your positive answer should have been this. If not, hit me up later. 7.78 seconds, 7.78 seconds. Oh, no, wait a minute. I'm not done. Emily, what was this question you asked me to find? Part A said find t. Part A said find t. Yeah, a little faster, ready? Part A said find that, range. Which, Brett, is actually d what? Now, dx. And as it turns out, Brett, dx is just Vxt. What happened to the half at? Oh, yeah, it cancels. Notice I'm taking a few more shortcuts now, right? It's going to be Vx, which was 15.78 times 7.78 times 15.78. And I get a lovely range of 122.8. Oh, no, three sig figs. I get 123 meters. Am I right? That would be a great written question for probably five marks. Very nice. What are you wanting? At what time does the projectile reach its maximum height? Oh, height, vertical, vertical, vertical. Really quickly, let's write down. Ay equals negative 9.8. vy initial was 32.36. They want me to find time. Oh, and there's one more thing I know. At the maximum height at the top, what do I know? vy final is 0. You know what I think? I can use the good old vf equals vf. I can use t equals vf minus vi all over 8. It equals 0 minus 32.36 all over negative 9.8. How long to get to the top? You get 3.3 bracket, 0 minus 32.36, close bracket, divided by negative 9.8. Show me the goods. 3.3 seconds. That's part one of part b. Joel, what's part two of part b? What's the second question they ask? How, what? Ah, you know what that is? That's saying, hey, find dy. So I'm looking for an equation that has d in it and then has av initial and t, or av initial and vf. I think I can just use plain old d equals vit plus 1 half a t squared, right? Do I know vy initial? Yep. Do I know the time? Just figured it out. Do I know a? Oh, this is plug and chug. V initial, 32.36, t 3.3 plus negative 4.9, 3.3 squared. Where's the negative 4.9? Oh, all right. That's right, half a. And you get 98.4, right? You get 98.4? I don't think you do get 98.4. In fact, I know you don't, people who are faking it on their calculators. What do you get? Louder, Katie. You get 53.4 meters. Why is that not the maximum height? Why is the actual answer 98.4, like I wrote in brackets? Matt, we're on a cliff. What we've just figured out is how high above your starting point you reached. You made it 53.4 meters above your starting point. But how high was your starting point, according to this question? How high was the cliff? D equals 45 plus 53.4. And that's where the 98.4 meters above the ground comes from. Question, Mitch? No? Question, Brett? Sure? Because you're drooling a little bit, looking a little befuddled. You good? You good? Sorry, the drool's just chronic. OK, my bad. C, yes. Can you know what the homework's going to be? Probably number one. Probably number two. Probably number three. Probably number four. Sure, six. Couldn't you just say, oh, Mr. N- Yeah, well, I could have. We're nearly done, OK? This is going to answer your questions. Folks, you want to watch the last few minutes of the lesson because I like this question. I like part C. I like this question. I like this question. I like this question. Why would I say I like this question so many times? Did I say that? Or are you just like, really? I never would tell you that. You're just a good student who notices things that teacher has emphasized. Good. Brett says, find the velocity at t equals 2.4 seconds, OK? If it took 3.3 seconds to get to the top at 2.4 seconds, is it on the way up or on the way down? It's on the way up. Here's what I think that velocity looks like. I think that velocity looks like that. And I think it's made up of two components, the horizontal velocity and, don't write this next part down, Vy at 2.4 seconds. I think however fast it's traveling vertically after 2.4 seconds, if I add those two together, that should give me my resultant. Except instead of calling it Vy 2.4, I'm just going to call it Vy final. Because that's where it's going to appear in my equation. I know this because it doesn't change the whole time. What was Vx? I've scrolled down. What was Vx? We calculated it at the top of this question. What was Vx? I think that was Vy initial, was it not? What was Vx? OK, don't get them mixed up. 15 point what? Sorry? 7, 8? The most common mistake is kids get this concept and they go, that's Vx, Vy. They put 32.36 right there. And they do the Pythagoras. And you know what they get as an answer? They get 36 meters per second at an angle of 64 degrees. They've just gone backwards and uncomponentized their velocity. Instead, what we need to do is we need to go vertical over here for a second. And we need to realize that Ay is negative 9.8. Vy initial, what's Vy initial, Nicole? 32.36. And this question told me that I want a time of 2.4 seconds. So I should be able to find Vy final. As a matter of fact, I have an equation that's already got it by itself. I think I can go Vy final equals Vy initial plus AT. It's going to be 32.36 plus negative 9.8 times 2.4. Question, Mitch? Is that OK? What is my after 2.4 seconds? I'm still traveling horizontally, because Vy.7.8. But what's my vertical velocity after 2.4 seconds? It's slowing down. What do you get? Sorry? Anybody else? 8.84? Probably depends whether you used a rounded off version or what. So 8.4, 8.34 meters, 8.84. Sorry, guys. 8.84 meters per second. By the way, what if I got a negative answer for Vy final? What would that tell me? It would tell me I should have drawn, instead of the blue line going upwards this way, I should have drawn the blue line going downwards this way. But it'll work still. Now, this is the velocity at 2.4 seconds. You good? How can I find this? By the way, when I had that stark realization, I probably also would have gotten a little shiver and like, oh, yeah, absolutely. I agree with that. So how can I find the magnitude of this velocity? What grade 8 math skill can I pull out of my back pocket? Well, let's do that. Velocity at 2.4 seconds is, and I'm going to do that all in my calculator. It's just I'm actually going to find the squared. What will I remember, Caitlin, before I'm done to do what? Yes. So the magnitude of the velocity I get is 18.1 meters per second. What angle will I use? Hey, how about that one right there? Jacob, can you help me out? Jacob, can you help me out? Thank you. You're back? Where were you? Oh. Jacob, opposite of Jason for hypotenuse. What trig function? What we do in Hawaii? Yes. In fact, the tangent of the mystery angle is going to be opposite over adjacent 8.84 over 15.78. How can I figure out the actual angle? Ah, nothing. How can I figure out the actual angle? Hey, inverse tan of 8.84 divided by 15.78. And I get 29 degrees. At 29 degrees. And we said last day we would say this as above the horizontal. Caitlin, does that answer your question? That's how I approach. If they want me to find the velocity in the projectile's flight at any time, I find the two components. The horizontal I've probably already found. The vertical, they're either going to tell me the time or breadth in question ten, which is a bit trickier. They told you how far to travel horizontally. And since you know the horizontal velocity, you can find how much time has elapsed. And then you'll know T. And you can plug it in to find BY final, add the components together, do the Pythagoras, and do the trig. What's your homework? 1 to 6, as well as the stuff from lesson 6. I have a couple of videos, but I'm going to show those next class because you guys are zoning out on me.