 Okay, red lane here So I'm gonna do a Critique I guess of a con video I just kind of picked one of random and I don't know how well this is gonna work and we just met but call me crazy so Let's see. I kind of picked one of random. It's a little bit longer than I wanted to I just looked at the time I love them 43, but you know what I'm just gonna go for so Hopefully the audio turns out okay, and the squeaking chair doesn't bother you too much You see okay, I can see okay Let's just play it. Let's just do this Agile question and the question is let's say I have a ledge here, and let's say it has height h So let's say it has a height over here And what I'm curious about is if I were to either let's say that this is me over here If I were to either jump myself Don't do that recommended for very large ages or if I were to throw something maybe a rock off of this ledge How fast would that either myself or would that rock be okay? I'm sorry. I have stopped one It's not really an interesting problem, and it were an age old question. That's not true to He automatically goes in there saying okay. Well if you throw a rock I Don't know how he's gonna solve the problem, but I suspect he's going to say drop the rock Which is a completely different problem Let's just go I Never gonna get through this thing is too long when it gets right before it hits right before it hits the ground And like all of the other videos we're doing on projectile motion right now We're going to ignore air resistance and for small ages and for small velocities That's actually reasonable if or if the object is very aerodynamic and has and it's kind of dense that the air resistance will Matter less if it's me kind of belly flopping from a high altitude then the air resistance will start to matter a lot But for the sake of simplicity, we're going to assume We're going to assume no air or we're not going to take it to affect the effects of air resistance Or we can assume that we're doing this on on a planet that has no atmosphere However, you want to do it. Let's just think I am impatient. It's my own That's not realistic, but this actually would be realistic for a small age if you were to jump off of a Is he still talking about air resistance? I really am impatient. People get impatient with me, too He still doesn't recommend it So let's just think about this a little bit we want to figure out we want to figure out so at the top of Right when the thing gets dropped right when the rock gets dropped you have an initial velocity You have an initial velocity Don't do that that's a scalar that's a vector scalar vector can he be equal cannot know bad zero vector Negative vector Okay, I mean I'm hyper analyzing this but Okay, you cannot do that. It's bad Negative vector is down bad. You can say the if it's moving down. It has a negative y component But then it's a scalar. We don't say this a vector going down is negative. That's not true. I Know that's okay I'm never gonna make it through this We're going on two and a half Have some final velocity here that is going to be a negative number Again value no get rid of the vector sign and put a y Negative Acceleration of gravity for an object of unfreefall They have an object in freefall near the surface of the earth. We know it and we're gonna assume that it's constant Say something about air again do it acceleration is going to be negative 9.8 meters per second square vector Given H and given that their initial velocity is zero and then our acceleration is negative 9.8 meters per squared We want to figure out what our final velocity is He said meters per square of those guys get the ground I'm going to assume that this is this H is given in meters right over here And we'll get an answer in meters per second for that final velocity. So let's see how we can figure it out So we know we know some basic things and the whole point of these is to really show you that you can always derive these more Interesting questions for very basic things that we know so we know that displacement is equal to Displacement is equal to average velocity average velocity times change in time Times change in time and we know that I think that's a velocity If we assume acceleration is constant, which we are doing average velocity is the final velocity Plus the initial velocity plus the initial velocity Over two and then our change in time our time or the amount of elapsed time that goes by This is our change in velocity. So elapsed time is the same thing All right over here is our change in velocity Divided by divided by our acceleration and just to make sure you understand this It just comes straight from the idea that acceleration That's not good. How do you do a vector divided by a vector? Times time or I should say acceleration times change times change in times If you divide both sides of these this equation by acceleration you get this right over here So that is what our displacement remember I want an expression for displacement in terms of the things So you should just at this point to say okay, boom We're gonna just deal one dimension and boom just use the y-portal and then you can do delta v Y divided by a y you can do that So this first expression for the example we're doing The average velocity is going to be our final velocity our final velocity divided by two Since our initial velocity is zero our change in velocity Change in velocity is the same thing Change in velocity is the same thing as final velocity minus initial velocity Minus initial velocity and once again, we know that the initial velocity is zero here Okay, this is just a little personal note and you know everyone has their own little quirks and I do my own done things too But he always says everything twice. He always says everything twice It's sort of like in Top Gun when they're fighting Fox to Fox to turning left breaking left, you know, that's what he does I don't know gets kind of annoying But like I said, I know that I'm annoying Change in velocity is the same thing as our final velocity So once again, this will be times instead of right change in a velocity here. We can just write our final velocity Because we're starting at zero that should be you can't say zero vector whatever our final velocity divided by our Acceleration by our acceleration final velocity same things change in the velocity because initial velocity was zero And all of this is going to be all of this is going to be our Displacement and now it looks like we have things in we have everything written in things we know So if we multiply both sides of this expression or both sides of this equation by two By two times our acceleration by two times our acceleration on that side multiply the left hand side by Two times our acceleration Two times our same said twice on the fucks to fucks to we get two times our acceleration times Times our displacement is going to be equal to on the right hand side To cancel out with the two the acceleration Acceleration it will be equal to the velocity our final velocity square and you multiply two vectors Stop time cross product our final velocity square final velocity how do you square vector? And so we can just solve for final velocity here So we know what our we know our acceleration is nine point is negative nine point eight meters per second squared So let me write this over here. So this is negative nine point eight So we have two times negative nine point eight so I can just let me just multiply that out So it's negative nineteen point six meters per second squared times meters per second squared And then our what's our displacement going to be what's the displacement over the course of dropping this rock off of this ledge or off of this roof So you might be tempted to say that our displacement is h But remember these are vector quantities So you want to make sure you get the direction right from where the rock started to where it ends I don't think I'm going to make it through I really don't How much more time do we have? Okay, I can make it and our convention is Down is negative. So in this example our displacement our displacement from what I randomly just picked us from two I didn't look for round the displacement is he going to be equal to negative age You know, I don't plan that far ahead distance of age But it's going to travel that distance downwards and that's why this vector notion is very important here our convention It's very important here vector or the scale over here is going to be It's going to be negative h and negative h meters. Okay. I don't think he's doing an important here, but This is this is the variable. This is the sort. Yeah, I wouldn't do that either H would be Lucky for 10 meters can't allow the meters is inside the variable h. I wouldn't put h m I mean, it's not technically wrong. I don't think but h Meter squared per second squared See, yeah, I wouldn't do that. I just wouldn't is equal to our final velocity And notice he made a big deal about vectors, but there's no vectors down here. It's like poof. Oh, no, there it is. Okay Notice when you square something you lose the sign information from final velocity was positive you square it You still get a positive value if it was negative and you square it you still get a positive value But remember in this example, we're going to be moving downwards. So we want okay So he made a big deal about the sign and then he says oh, you don't even know the sign We take the essentially the negative square root of both sides of this equation What does that mean if the sign doesn't matter? What does that tell you sides of this? So you take the square to that side you take the square to that side you will get and I'll flip them around You'll get your the velocity. Oh, I guess the negative sign says he can take square root of positive number, but Still the square root of 19.6 h and you know You can even take the square root of the meter squared per second squared Treat them treat them almost like variables even though they're units And they are the radical sign variables meters A meters per second and the thing I want to be careful here is if we just take the principle root here The principle root here is the positive square root But we know that our velocity is going to be downwards here because that is our convention So we want to have we want to make sure we get the negative Square root so let's try it out with some numbers We've essentially solved what we set out to solve at the beginning of this video How fast would we be falling as a function of the height? But let's try it out with some things. Let's say that the height is I don't know. Let's say the height is let's say the height is five meters Five meters, which would be probably jumping off of a Or throwing a rock off of a one story dropping a rock story building dropping. It's about that's about what would happen if you throw it Then this well, I don't even want to point this stuff but And so what do we get if we put five meters in here? We get 19.6 19.6 times five times five Gives us 98 so almost a hundred almost a hundred and then we want to take the square root of that It's going to be almost 10 so square root of 98 It gives us nine point roughly nine point nine and we want the negative square root of that So in that situation when the height is five meters So if you jump off of a one-story commercial building You're going right at the bottom or if you throw a rock on that right at the bottom right off the ground It will have a velocity It will have a velocity of negative nine point nine I would love to see him say something about why we're looking at right before it hits the ground I mean it's important Instead of after it's a ground as an exercise to figure out how fast this is in either kilometers per hour or miles per hour It's pretty fast. It's like, you know, it's not something you would want to do And this is just something one-story building But you can really figure this out You can use this for really any height as long as we're reasonably close to the surface of This is is a good start. That's not the way I would really encourage it I think you made a little short here that makes it a little confusing. We'll start to matter a lot whatever I made it. Yes. Okay. So I think the biggest problem If I had to grade this as a if it was a student turning this in I would say you're confusing vectors and scalars and that's a bad thing The the the other thing was it not necessarily wrong as much as It really wasn't an interesting problem But uh, so then then someone's going to say well you if you think it's not good You should do something better. So I think I'll do that I think I'll solve this exact same problem and make a video of it and just just for comparison