 Hey everybody, welcome to Tutor Terrific. Here we have our second lesson in our chapter three of my physics course We're looking at kinematics in two dimensions and today We're going to really really really study the type of motion that we're really going to focus on for this whole chapter of projectile motion We're going to review components of vectors and look at something called range as well. All right, let's begin So what I want you to do first is to describe this trajectory here I don't know if it's clear to you, but someone behind this black curtain has tossed a tennis ball in the air and taken many photos and superimposed them on each other at equal intervals, so it's like a fast-motion camera and This is what the tennis ball would do after it's let go by the person throwing it. Can you describe this trajectory for me? What are some of its characteristics? What do you notice about it? It looks like to me that The tennis ball seems to glide back down to earth in a very particular Pattern, so the trajectory has a certain shape to it. It appears as those as time goes on In the second half the ball seems to fall at a faster and faster rate towards the earth and it seems to turn around at some height and Also when I'm looking horizontally at the tennis ball just its horizontal distances between these picture frames that the distance seems to be pretty much Constant horizontally speaking, but vertically speaking. It's definitely not constant So what's the shape first? Let's start with the shape Anybody recognize this shape from their math classes If you're not sure, let me give you a list of possible shapes. It could be Okay, here's some basic functions in math. It looks like one of these shapes. I'll be at upside down and That would be this one here the quadratic x squared Except upside down. What's the other name for this? It's problem. Well, that is the shape of all these trajectories when something is in mid-air and it's Go undergoing free fall. It's the shape is a parabola or a section of a parabola Okay, now obviously since the velocity is changing at least vertically speaking it seems there must be an acceleration Well, what acceleration is causing that motion? If you remember from previous classes, it's got to be gravity gravity is acting on That tennis ball and it's acting on anything that's in the air that is in free fall What we call this specifically is we call this projectile motion projectiles Some people call it parabolic motion as well But the common name used is projectile motion and anything that is the undergoing free fall is a projectile So that's what we give it the name It's always in this upside down parable parabola shape, excuse me, and if no other forces are acting It's a perfect parabolic shape All right the motion In an object in two or more dimensions such that the acceleration is only due to gravity and is constant is the formal definition of projectile motion So if I were to draw the acceleration vector at each of these snapshots They would all look identical And it all point directly downward and their magnitude would all be g which is 9.8 meters per second squared near the earth's surface So this is the acceleration that is responsible for this type of motion Now let's look at the basics of this particular Shape and this particular Trajectory so the parabola is the trajectory shape specifically There will be for each projectile an initial velocity. Okay, and here this red vector in this picture is that initial velocity There is a launch angle associated with The initial velocity vector with respect to the horizontal and we need to know that and It's usually Denoted with respect to the horizontal like this angle here The initial height is also an important factor as we will see For that the projectile for example this football is not on the ground when it's thrown But eventually reaches the ground later the horizontal distance covered before the Projectile reaches the ground is called the range. We have a special formula for that that we'll learn later But that is the idea of The horizontal displacement only not the vertical displacement the horizontal is called the range Now that velocity vector is at an angle and as you might have guessed we didn't just learn Component in the last lesson for no reason We are going to split vectors at an angle velocity vectors, especially initial velocity vectors into components So let's just review here. We've got this Velocity vector that's 12 meters per second at a 32 degree angle And I've shown you that components here the horizontal component and the vertical component what they look like What are their values? We're going to resolve this vector v into components right now Well, the horizontal component will be the total magnitude times the cosine of 32 degrees okay, and that would be about 10 meters per second with proper sig figs and Then the vertical component here will be 12 meters per second times the sine of 32 degrees which will be less In about 6.4 meters per second. I'm about half of the total magnitude So just review that we are you're not going to do that this chapter. You're going to be definitely Resolving these vectors into components at an angle. Okay. Can you apply the knowledge of components at least conceptually in the following situation? So, let's say you've got here a You've got a cannon that shoots a cannon ball directly horizontally off a cliff from the edge of the cliff Okay, I want you guys to determine what the components of the velocity not the entire velocity vector But the components of the velocity vector would be what they would look like at each of these snapshots Okay, right now we have the total velocity vectors for you As you can see they increase in size but When you draw the components, I want you to determine what they would look like Okay, so to pause this video take a minute and this is a good exercise for you and draw these One two three four five six cannonball pieces the last one it has not yet hit the ground This is the instant before it hits the ground below And try and draw the components of the velocity horizontal and vertical components for each of these snapshots So take a minute to pause right now. So now that you are back. Let's see if you Have got this right. This is what it should look like. Okay. I'm not looking for magnitudes here I'm showing you what the magnitudes would be if the initial is 20 meters per second Notice how if this is done correctly the vertical component continues to increase in magnitude, but the horizontal component is constant the horizontal component stays constant Its initial value is its final value and its value everywhere, but Every second in time and you can see here. We've got 9 negative 9.8 meters per second for the first v y a second later would be the Time distance then between these two snapshots and all the other snapshots look at how it's increasing multiples of 9.8 and They're all negative because they're pointing down, but Vx is constant This is what the components look like for projectile motion when we start directly horizontal Okay, the horizontal component isn't changing at all I'm going to animate this motion for you so you can see this in a more animated sort of video format There we go As you could see This is a little bit Many more snapshots were taken, but as you can see the v y down here is constantly increasing each second It's about 10 meters per second faster. That's about 9.8 But Vx is constant in this case. It's a constant 100 meters per second And I'll just show this one more time You can see that vertical velocity vector growing in size, but the horizontal velocity vector is not Changing, okay, so we need to practice this more. I'm going to give you a slightly different situation What if we have a projectile that's launched from the ground and not from the top of a cliff up at an angle? So what I want you to do is draw what the components of velocity would look like in this case We're launched at some angle upwards And we turn all the way back around and come down to the same vertical position some horizontal position over Okay, I want you to draw take take a minute to pause this video and draw the Components of velocity for this situation pause the video now Okay, so let's see what you're able to come up with If you came up with anything like this You're doing well. You're starting to understand this material the Velocity x components should all be constant. They should all be pointing to the right the vertical velocities Should always should all be different for each snapshot They should start by pointing upwards and be large and as you get higher up. They should decrease in size and Then at the very top you should have no vertical velocity because we are turning around Vertically speaking and then as we start to fall our vertical velocity grows in size This is what will occur when there is a constant downward acceleration equal to g It's constant. This is the type of motion you will receive And you can see this is a parabola parabolic motion a projectiles motion Okay, so I'm going to animate this motion for you. I notice this is a slightly different situation here But it still works You can see the vertical velocity vector Decreases upwards and then starts to decrease downwards being zero at the very top and notice how the Horizontal velocity component is constant. It does not change. It's always 60 meters per second in this case and the v y starts being 60 and then Completely becomes negative and grows in size about 10 meters per second per second, which is about the value of g So one more time look at that This is what occurs in projectile motion. Okay, this is the type of Velocity vector components that we will always have they will always follow this sort of trajectory and this sort of Idea for change okay vx does not change v y is undergoing an acceleration downward that is constant, okay So let's look at the basics of what we learned Here's another snapshot for you This one of course also shows the total velocity vector at the same time as the component so you can really see how it's related to the components So first of all Acceleration that causes this motion is due only to gravity We have to ignore air resistance and other things like that and there's no other Accelerations involved the direction of the acceleration if we are talking about normal situations for an intro trick physics course Would be near the center of the earth it will point downward and constant at all times I have not drawn the acceleration vector for these snapshots just the velocity Okay, it only affects the vertical component of the velocity since it points constantly downward As you can see here v y is the only component that is changing vx is constant Okay, vx horizontal component velocity will remain constant these are the properties these are the Important facts about projectile motion that you need to know All right All of this all of this right here is what leads to this general shape for this trajectory The overall shape being a parabolic parabolic parabolic shape Okay, and it's usually an upside down a parabola or a section of an upside down parabola That's the shape of the trajectory All right now a thought experiment for you guys We're going to discuss This machine up here Again equal timestamp snapshots were taking of an orange excuse me a red and a yellow ball Okay, the red ball was dropped directly downward with no initial velocity as you can see here The yellow ball was launched with a specific initial horizontal velocity And it left the machine at the exact same time that the red ball did okay, and we can see that their snapshots There's the same number of snapshots for both. Okay So I have a question for you my first question is this which ball reaches the ground first Look closely at these snapshots both balls were released at the same time and Pictures of them both were taken at the same time. I'm not sure the Distance between the photos, but they were taken at equal time intervals Which ball reaches the ground first take a minute to think about that if you look at the snapshots you seem to See that they're each vertically They're horizontally separated by a greater and greater amount, but they're not vertically separated at all each Snapshot shows the tennis balls or whatever balls these are at the same height at the same time Basically, okay within the margin of error And so if this is the ground right here you could tell they're both going to hit the ground at the same time Why does this make sense? This makes sense because they are undergoing the same acceleration It's all vertical and their initial vertical velocities were the same zero Because of that they will reach the ground at the same time their vertical components of velocity will always be the same So another question I have for you. I'm sorry that the answer is already there. Which ball has a higher Vertical excuse me horizontal component of velocity when it reaches the ground now the red ball as you could see has no Horizontal component of velocity because it has the same horizontal position as it falls So it can't be the red one the yellow one has a higher Horizontal component of velocity because it has one at all it has the same one as It stays constant if we ignore air resistance. I know this probably wasn't done in a vacuum chamber So there is air, but all intents and purposes. It's constant and so The yellow one will have a higher horizontal component of velocity Vx when it reaches the ground It has some constant non-zero Horizontal component of velocity one last question Which ball has a higher Magnitude of total velocity when it reaches the ground so which one's total velocity vector is bigger Take a minute to think about that The red one has no Horizontal velocity the yellow one has a horizontal constant velocity and both of them have a Vertical velocity which is the same at each instant in time Well as you might have guessed that means that the yellow one will have a total higher Magnitude of velocity, so if you're to be struck by the yellow ball It might hurt a slight bit more than being struck by the red ball all right guys, thank you so much for watching this video a little overview on Projectile motion, which is the kind of motion we are going to be studying For the rest of this chapter. I know there's lots of different types of two-dimensional motion out there But we're going to study projectile motion specifically in this chapter. Thanks so much for watching guys. This is Falconator signing out