 Mr. Duck. Yes, Cody. I can't help noticing that your title says lesson six projectile motion part two I don't really recall a projectile motion part one Maybe when I was typing them this summer. Mr. Do it got the titles mixed up and really we should be doing that, please Lesson five projectile motion part one. Let's call it that please and Then tomorrow you lesson five, which is actually going to be less than six What's a projectile a projectile is an object in free fall Dropping something is technically a projectile, but we did do that last year. We did free fall what we're going to add this year is sideways motion to the projectile But we're going to be in our magic physics world We're going to ignore air resistance Tennis balls have a fair bit of air resistance when they get going really fast and you do the plate tennis No, you can put a pretty nasty curve on these things with a slice Base balls are a little better the cross balls are really nice Not much air resistance or a pick a solid metal sphere. That's what we're kind of using in our minds Mathematically, but we'll be demoing off and with stuff that has air resistance. We're going to ignore the air resistance to make the math What we want you to realize is there are two things going on with any projectile a projectile is traveling in two directions It's traveling horizontally Yes, you saw it But also it's traveling vertically which you were probably able to see better because what's coming straight towards you But you saw it go up and go back down and come towards you But the only way you could tell was coming towards you was because it was getting bigger in your eyes If you were really far away, you wouldn't be able to tell Thank you for avoiding the tablet by the way Be Relax Relax Sorry for the interruptions those who that are online a projectile is launched through the air any object that's launched through the area if we ignore air resistance However, we have to get rid of some misconceptions and this is the first one This comes from the fact that you folks have watched cartoons example one says this A mass is held at shoulder level and it's fired horizontally Which curve best shows the path it follows to the ground? Path a straight down path B Path C it goes straight for a bit and then goes straight down path D It goes straight and then drops straight down and once again like always you're going to vote How high you hold your hand up is how certain you are of the answer. I'm positive I'm pretty sure I'm only voting because mr. Dukes keeping track of the faces and if I don't vote. He'll make fit one of me Okay, so you're ready who says path a Who says path B? Who says path C? Who says path D so we're about split between C and D for the most part So you can either defend your choice or attack someone else's choice attack or defend who's right or who's wrong convince me Carson see see is because of cartoon physics As soon as you fight and see is because you guys understand how white bulls work because the movies get it wrong If you're firing a rifle for example the split second that leaves the barrel It's dropping. It's falling. It doesn't travel straight for a while because it's like going so fast that gravity doesn't defect it Some that's not how it works Okay, and again, we're not talking about something like a frisbee which has a different type of aerodynamics with the air resistance We're talking about nice round aerodynamic projectiles. Yeah, the correct answer here is Be you want to test that you say there enough? So right now I'm gonna aim this for Spencer's head And it's about the same it's about horizontal now Spencer behind you this little chair Can you grab that chair for protection, please? It be sorry if see is correct. This should also travel pretty much straight But you can see it dropped about just in that short time about that much it wasn't free folks As Soon as a projectile is launched as soon as it's launched it's accelerating at negative 9.8 meters per second squared down So defend your answer. Have I convinced you that we're not good at well? a equals negative 9.8 meters per second squared down immediately Do they still show the old coyote Roadrunner cartoons? Those are the worst ones because he always runs off the cliff He hovers there for a while until he figures out that he's in free fall and then he's in free fall right through Roadrunner physics bad physics example to Suppose I had two identical objects suppose I took my Nerf dart gun and I held it horizontal and I also just held a Nerf dart in my other hand And I dropped this dart at the same time as I pulled the trigger. What would happen? Which would hit the ground first? Object one since it has a more direct path Object to since it's moving faster than object one or see they both hit at the same time What do you think Tyson? See, I'm not sure what sorry Convince me if I summarize Tyson's argument It's the answer is C because C is the right answer. I'm gonna go a little more detailed than that I know wonderfully, I'm gonna reference that. Thank you for beating me to the punch captain. Yes This is the key idea behind projectiles Shannon what we're going to do from now on whenever we think about a projectile We're gonna think of it as having two components horizontal and vertical and Vertically all projectiles fall at the same time and yes Mythbusters did a lovely episode where they took a rifle in a long long warehouse And they fired the rifle and they measured where the bullet landed And then they redid that but they put a camera right where the bullet had landed and put another bullet Just hovering on a magnet at the same height as the rifle so that when you pulled the trigger The magnet turned off and the bullet from the magnet would drop as the rifle bullet was fired And sure enough they hit the ground. I think it was in about point two of you point zero zero two of each other There is some air resistance in the real life world that Comes into effect, but all objects fall and free fall at the same rate. That's what Galileo came up with So the answer here is gonna be they both hit at the same time There is kind of mr. Kimose have that little demo thingy Where it fires the ball and drops the ball. I've tried that I can never get it to work So I'm not I didn't bother getting it out this morning I can never get a level and yeah, I got a different demo to show you guys later okay That's going to be really handy then because anytime we launch something horizontally off a cliff Mathematically Alexis we're going to pretend it's just falling straight down for a big chunk of it And it'll give us lots of ways to analyze it. What this important demonstration shows us is that the horizontal and the vertical motions or components of a projectile are Independent of each other In fact when we solve a projectile question Ashley, we're going to draw a line down the middle of the page I'm going to call one side horizontal. I'm going to call one side vertical I'm going to write down two things right away always We'll talk about what those two things are and then I'm going to just ask what information do I have that's going to determine Whether I solve or analyze this projectile horizontally or vertically If you remember the Nerf dart gun that I shot Justin if you had had a strobe light that flashed every second or every tenth of a second And you've been able to take a picture every tenth of a second I did find a great picture online But when I it was actual photo strobe But when I put it into this document and tried photocopying it just became one of those big smear black Diagram didn't it didn't translate from the internet So I found this one, which is a computer graphics one If you look at any projectile and you take a picture, let's say every tenth of a second You'll find that the horizontal distance it travels is constant But the vertical distance that it travels is increasing What this really means is now my abbreviation for vertical velocity is vy vy is Negative increasing You know what I mean by negative increasing which way is it increasing in what direction down? I just don't feel like right negative because The vertical acceleration is negative 9.8 meters per second squared We all remember that number from last year gene we called it But the horizontal velocity if we ignore air resistance and we're going to The horizontal velocity and I'm going to call that Ashley vx is Constant your horizontal acceleration is zero What that means Cody is if I was on a skateboard Or I'm just going to walk at a constant speed and I throw something straight up It'll come right back down to my hand even though I'm moving forward It won't land behind me or in front of me. It's going to keep moving at exactly the same speed That I'm moving at Is constant There's a wonderful demo We have a cheap version of a little cart that you can roll and it fires a little ball in the air It's supposed to come straight down again again. I've never been able to get that one to work out worth a dime I have a better version right now. It's a video put your pencils down, please Much better equipment than I have I would love to own some of that stuff, but that's okay. They're MIT. They got a budget turn the page Spencer catch and back Now let's suppose one third of the way towards me. We froze time And we made the ball just freeze for a split second. What are the forces acting on that ball get the obvious ones? Gravity what else? I can't hear you. Is Spencer still touching it? That he can't possibly be exerting a force on it. What are the forces acting on the ball? And the answer is if we're ignoring air resistance only gravity Only gravity what direction does gravity act in? Down so the reason vx the horizontal is constant and v y the vertical is changing is Did I turn the video back on? I think I did Yes, I did good only one force Gravity and gravity is vertical gravity can't possibly make it go faster sideways That bugs people because they're like Tyson suggests it's moving there has to be a fork Don't know if it's at a constant speed Newton's first law said an object can continue moving at a constant speed and no force is acting on it and Again in real life air resistance is technically slowing it down a bit So it's pretend we're in a vacuum or on the moon example for consider this stop action picture It says at each point along the path indicate the velocity components. Let's do vertical velocities first So we're gonna launch something up at an angle Okay Right when I pull a trigger That projectile that nerf dart is moving Horizontally and vertically and the vertical component is at its biggest You know how I know because on the way up what happens to projectiles vertical speed on the way up Slows down so Cody if I was gonna draw the vertical component right here. It'll be a shorter arrow than this one Oh, and at the very very top for a split second Cody. What's the vertical component trick question? For a split second the vertical component is zero and then on the way down It's getting bigger, but negative and not only that if we start and end at the same height You know what you can tell me about the final vertical speed It's exactly same as the initial vertical speed, but negative Ashley if it went up at 20 meters per second Coming back down at 20 minutes per second What about the horizontal velocity What about the horizontal velocity well, it turns out the horizontal velocity is constant is constant is Constant is constant. It's a vector arrow the same length as the original That was that video demo that we just showed you when you're from a cliff it gets a bit trickier And that's gonna be the toughest questions. We're going to do in this unit launching from an a cliff at an angle Says indicate velocity components in the stop action picture and then fill in the key facts at the top What do I know? Cody, I know that v y is 0 now. I would break this projectile into Vx and Vy initial Spencer, why did I put an initial on the v y but I didn't put an initial on the vx Why would I have done that? You knew I could count on you because vx isn't changing So why would I put an initial because initial is the same as final horizontally isn't going to change Vertically is going to change. In fact, you know what when you're even with launch The vertical velocity is going to be negative the initial vertical velocity When it gets back to the same height it's traveling at the same speed as it started But now it continues to fall so person if it continues to fall what's going to happen to the vertical velocity? It continues to fall. What's going to happen to its vertical velocity? Just slow down or speed up Yeah, why? Grab it. It's got a force acting on it. Okay, so the final vertical velocity Would probably look something like that. Oh and if I add My horizontal that it's been traveling the whole time The actual impact velocity Would be that vector right there if you add v y final plus Vx tip to tail There is your impact velocity magnitude and direction Now the good news here is hey, it's right angle triangle. So the trig isn't too bad Horizontal speed is blank because blank vertical speed is blank because blank horizontal speed is constant vertical speed is changing Why is horizontal speed constant? Because there's no horizontal acceleration Why is that because there's no horizontal forces once Spencer lets the ball go Tyson? He has no longer any impact on that projectile Vertical speed is changing. You know why because there is a vertical acceleration and in fact, I know what it is exactly How big is it? Yeah Because a y is negative 9.8. That's the acceleration and Kirsten which force is it that's providing the acceleration You said it gravity yep, and Then here's the final key vertical and horizontal motions are Independent what that means is they don't affect each other. Don't you dare put a 9.8 into a horizontal equation Uh-uh no, no turn the page. So the first type of projectile we're going to look at is Launched horizontally from a cliff So you're not launched from the ground you're launched from a cliff, but you're not launched at an angle You're launched horizontally And here's a specific example our horizontal velocity is 20 meters per second and the cliff is 50 meters high Lovely diagram and it says fill in the appropriate chart now if that chart wasn't there I would create it I would draw a line down the middle. I would call one side horizontal and I would call one side vertical But they've already put the chart there for me All right horizontally These are the first two things I always fill out the accelerations What's the horizontal acceleration? It's a trick question Zero what's the vertical acceleration? It's not a trick question, but it's supposed to be an easy question negative 9.8 In fact, I usually do those before I do anything else and I remember a for acceleration a is the first letter the alphabet is first thing I do a acceleration Velocities What's my initial horizontal velocity? Look at my diagram. How fast we traveling horizontally the split second. We need the cliff 20 fact I don't like the fact that they called it VI. I'm just going to call it Vx Because I suggest that it might be changing. It's not you know how I know it's not because of that Now here's we have to put our thinking caps on just a little bit The split second I leave my cliff. What's my vertical velocity? Zero you know why have it started falling yet That's only if we're firing something horizontally for a split second hasn't dropped yet. I know one more thing What's my displacement? Vertically I can get that from the diagram. I'll give you a hint. It's not 50 My distance is 50 What's my displacement? It's not 50 Why is it negative 50 am I ending up above from where I started or below from where I started Cassidy, how many different quantities do I know in my horizontal? How many do I know in my vertical? Where do you think I'm going to start solving stuff then I got more stuff to work with in the vertical? Okay, example 7 says use the values of example 5. I think it means example 6. Yes, whoops To find the flight time and the range of the projectile So really quickly. I'm just going to rewrite these values. It was 20 zero Zero negative 9.8 and negative 50. What do they want me to find first here to find the what? flight time I Only have two things. I can't find tea from here, but I have three things. I think I can find tea From here. So from your formula sheet. Can you find me an equation that has vi a D and T in it which one? Vf equals vi plus at no, I don't know the f Vf squared equals vi squared plus 2 ad. No, I don't know the yeah Alex which one? Yeah, the old favorite D is equal to vi T Plus one half a T squared. Oh And you know what? Alex, why can I do this? Why can I do that? Vertically vi is zero which makes this an even easier equation to solve Otherwise, this would be a quadratic and I'm having to pull out the quadratic formula. Yeah Now my equation is actually just D equals a T squared over 2 Andrew the over 2 came from it's a half. I can get the T by itself pretty easy move the 2 to the top Right Rob move the a to the bottom Right and how to get rid of squared Square root fact. I'm gonna argue that T is going to be the square root of 2 D over a and now it's plug-and-chug T is equal to the square root of 2 times negative 50 All over negative 9.8 By the way Remember when I said what's the vertical distance and some of you said 50 if you didn't realize below coding means negative If you missed that you'd catch it here because if you didn't have a negative there You'd be trying to take the square root of a negative and your calculator would barf at you and you'd go something's wrong But here I have a negative divided by negative two times 50 is a hundred divided by 9.8. It's gonna be a little bit bigger than 3.3.1 or 3.2 3.2 I'm gonna Now I'm guessing 3.2 3 ish. What what is it? Sorry 3.19. Ah, it's close 3.19 Alex units careful Look at the variable. Come on. Don't let me down here 3.19 seconds I'll keep the longer number on my calculator because I'm probably going to use that but the two or three sig figs If you put one nine seconds So how long was it in free fall vertically for? Answer Alex not this Alex not that Alex, but this Alex How long was it in free fall for? 3.19 seconds Alex how long was it moving sideways for? That's the beauty see now I have time now Boom right away I can write the same time over here because the vertical time of flight has to be the horizontal time of flight Ashley, why is that so helpful? How many different quantities do I have now in my horizontal section Cassidy? Now I can work with any three I can find the fourth But we don't have any formulas that only have two and find the third So what else did the what was the second thing flight time and The range what's the range? It's a new vocabulary word. Look at your diagram. What's the range? Yeah In fact, you know how I abbreviate range DX instead of dy DX equals So I'm looking for an equation that has vi a t and d in it Is there one? Oh same one. Oh, what can I cross out? Oh, I like that Why because horizontally the acceleration is what Simran? Because now this is really plug-and-chug The horizontal distance the range is going to be vi which vi. Well, what letter is right there? Horizontal the range 20 times the time 3.19 20 times 3 is 60 60 just below 64. I'm going to say 63.9 63.8 You know what probably depends whether you use 3.19 or the full t value that's on your calculator Full one is 0.9. Then I'm going to go with that one because that's what I was doing in my head You know, right Getting old so I'm trying to keep the brain active Trying to get back to doing some arithmetic in my head I had a college prop my physics prop was amazing He would get four or five sig figs with trig functions and cube roots But he had grown up without a calculator and growing up with a calculator You learn lots of shortcuts just as a matter of survival because Oh, you don't have to be looking stuff up all the time turn the page so we just did horizontally off a cliff He idea horizontally Vx is your velocity vy initial is zero What if we're launching from the ground well horizontally from the ground it'd be boring because it hit the ground right away We're gonna add an angle from the ground What's the velocity of this particular projectile? a hundred At what angle Shannon? 35 degrees We are never going to use that hundred to actually calculate stuff We're only going to use that 100 in the very first step And our very first step as soon as they give me a projectile at an angle my very first step is to Break it into the horizontal velocity And the vertical velocity Hey, Cassidy, how come I didn't put an eye right there? Sorry, how come I didn't put an eye right there? It's never changing. Yeah, that one is always want to remind myself And let's do a little bit of trig Cassidy this vx opposite adjacent or hypotenuse This 100 which trig function? Uh, yeah Oz right? Uh Oh coast yeah So if I hear you correctly Coast of 35 Equals vx over 100. What's vx? Coast of 30 is 0.86 so that'd be 86 coast of 35 83 82 yes, I don't know Here we take 81.9. That was a fluke that I won't take credit for Cassidy it's so good, uh opposite adjacent hypotenuse Which trig function In fact call me silly. I think it would be this same equation, but instead of coast what would be there In fact the work would be uh vx 100 times sign Oh I'm not gonna write that. Well, okay fine. I will I saw somebody go glazed here Sign 35 Equals vy times 100 Justin what'd you get? 7.4. Is he right? I will use these. I will never use the 100 for the rest of this question Will not now What was vy which trig function found vy? sign vy was sign vy was sign It would be great if there was some really dumb easy way that I could just maybe memorize that vy Was sign If I was a good teacher, I'm sure I could go up with something, but I got nothing for you By the way, you don't have to memorize that because it takes all of one second to derive But you'll be doing it so often if you're looking for a dumb way to memorize it. There it is You ready? Now let's analyze this projectile We're gonna break it up into horizontal and vertical and as soon as I break it up into horizontal and vertical I say a is what a is what? Horizontally a is Too slow horizontally a is Yes vertically a is The other reason I like writing that down right away Even before I even hardly read the question is my question's no longer blank. I feel better. I've written something My stress level's gone down Oh, I know a couple of more things What's vx? 81.9 What's vy? initial 57.4 And then there is one more thing that I know which can come in handy I know my displacement vertically How high was I when I started? Zero how high was I when I finished? Zero what's my vertical displacement vertically? How far are we traveled mathematically? This sometimes comes in handy Only works tyson from ground to ground not from ground to cliff Not from ground to cliff Only from ground to ground Example nine wants us to solve or analyze the projectile So for the projectile in question eight it says solve for the time to talk Let's quickly fill in the stuff we just had we said a was zero a was negative 9.8 a was 81.9 a Sorry a v was and v was 57.4 and What does part a ask us time to the What does it want us to find time to the Top what do you think is that vertical or horizontal the word top? What would that suggest to you mission? So i'm going to solve the rest of it Part a Here vertical Okay How many pieces of information do I have right now he's under vertical? Not enough Okay at the top is there anything else I know at the top Oh, there was something actually I think kody pointed out earlier at the top What What's zero? I got to be fussy v y final Is zero at the top He should now how many things do I know? That's enough to find a fourth So if I want to find time i'm looking for an equation that has a v i v f and t in it And do me a favor when you find it Read it to me getting the t by itself in your head because Yeah, that's that one Go for it Right via equals vi plus at and rewrite By the way, if you have include in you'll find for most lessons. It's helpful to have your formula sheet in front of you That's why I gave it to one for the test and one to just use your favor v f zero minus vi 57.4 all over Negative 9.8 am I going to get a negative oh no the top will be negative as well as the bottom I'll get a positive time What's the time of flight? Zero minus 57 is negative 57.4 divided by negative 9.8 negative 9.8 is close to 10 It's going to be close to negative it's going to be close to 5.7 a little bigger than 5.5 I'm going to go 5 9 that's a guess 5.86 okay I want to roll And I'm not even cheating often if I've done the lesson earlier. I can remember the answer for this time I can't time of flight 5.86 seconds check No, that's not time of flight. That's time to top B wants the time of flight. How can I find B fairly easily actually just Okay, now that only works because we're starting on the ground and ending up on the On the ground if we went from a cliff to the ground you can't times by two because going up is going to be shorter than going down So make sure you don't just say all right double it. No, but this one absolutely 5.86 times 2 is going to be 10 plus 11 points 11.72 That's what I said 11.71 11.7 because that's it two or three sig figs Ha, so I was right Alex, let's see asking What's part what's c want us to find? Ah, what's the ring? Oh, that's we said another Dx now. I'm going to walk over here to horizontal, but you know what before I write down dx What did I just figure out in B part B? What did I just figure out Alex? Ah, that means that's also the time of flight here because whatever it was traveling vertically That's how far it was traveling horizontally and now I can try and find the range I'm looking for an equation that has a v t and d in it One I agree. Oh, but you know what I can cancel out the half at squared again Oh, this is like Christmas in September You mean it's just v i t and the plus a half at square just cancels because there's a is zero now I can't remember. I said this already Courtney the most common error that kids do Is they say I don't know what the acceleration is they forget that at zero and so you know what they put there instead A vertical into a horizontal equation Don't do that Right the whole point of the vector math that we've done is for also us to realize Verticals can't go into horizontals and vice versa The range is going to be Initial velocity 81.9 times 11.7. Well 80 times 12 Would be eight times 12 is I don't know. What is it 958 units meters 158 meters sorry You know what it probably depends whether you use the 11.7 or whether you kept the full decimal Yep, and I when I mark these I take both By the way, yours I like yours better. I never round off you guys have can't Calculators that will store answers do that. Why round off and then use that to find an answer that's now wrong Turn the page Cliffs are where we're going to begin next class. We're going to pause here But right now here are the questions that you're capable of doing Now i'm going to be assigning more questions than just this from this exercise But for now you can do number one horizontally off a cliff There's four different questions to try with different v is and different heights And you can do At an angle from the ground to the ground Can't do number three yet four five and six are still a bit tricky as is seven and eight I haven't talked about number ten, but See if you can figure it out. If not, I'll be doing an actual example of it next lesson or the lesson after And so I assigned right now one two ten eleven Okay