Projectile motion graphs

so in each of these pictures we have a different scenario we have someone standing at the edge of a cliff on earth and in this first scenario they are launching a projectile up into the air in this one they're just throwing it straight out they're not throwing it up or down but just straight out and here they're throwing the projectile at an angle downwards and so what we're gonna do in this video is think about for each of these initial velocity vectors what would the acceleration versus time the velocity versus time and the position versus time grass look like in both the Y and the X directions so I encourage you to pause this video and think about it on your own or even take out some paper and try to solve it before I work through it so let's first think about acceleration in the vertical dimension acceleration in the Y direction we're assuming we're on earth and we're going to ignore air resistance we can assume we're in some type of a laboratory vacuum and this person has maybe an astronaut suit on even though they're out on earth what would be the acceleration in the vertical direction well the acceleration due to gravity will be downwards and it's going to be constant we're going to assume constant acceleration so the acceleration is going to look like this and if the magnitude of the acceleration due to gravity is G we could call this negative G to show that it is a downward acceleration once the projectile is let loose that's the way it's going to be accelerated now what about in the X direction well if we assume no air resistance then there's not going to be any acceleration or deceleration in the X direction so it's just going to be it's just going to stay right at zero and it's not going to change and what I've just drawn here is going to be true for all three of these scenarios because the direction and with which you throw it that doesn't somehow affect the acceleration due to gravity once the ball is actually out of your hands so now let's think about velocity so what is going to be the velocity in the Y direction for this first scenario well we could take our initial velocity vector that has this velocity and angle and break it up into its Y and X components so this be its y-component you just take the top part of this vector right over here the head of it and go to the left and so that would be the magnitude of its y-component and then this would be the magnitude of its X component so the Y component it starts positive so it's like that but remember our acceleration is a constant negative so our velocity is going to decrease at a constant rate so our velocity in this first scenario is going to look something is going to look something like that now what about the velocity in the X direction we see that it starts positive so it's going to start positive and if we're in a world with no air resistance well then it's just going to stay positive notice we have zero acceleration so our velocity is just going to stay positive one of the things to really keep in mind when we start doing two-dimensional projectile motion like we're doing right over here is once you break down your vectors into x and y components you can treat them completely independently that something will decelerate in the Y direction but it doesn't mean that it's going to decelerate in the X direction now what would the velocities look like for this blue scenario well our velocity in our Y direction we start off no velocity in our Y direction so it's going to be right over here but then we are going to be accelerated downward so our velocity is going to get more and more and more and negative as time passes and notice the slope on these two lines are the same because the rate of acceleration is the same even though you had a different starting point now what about the velocity in the X direction here it looks like this X initial velocity is a little bit more than this one so maybe it's a little bit higher but it stays constant once again now let's look at this third scenario in this third scenario what is our Y velocity our initial y velocity well it would look something like that and our initial X velocity would look something like that if we were to break things down into their components so our Y velocity is starting negative is starting negative and it's just going to get more and more negative once the individual let's go the ball because you have that constant acceleration that negative acceleration so it's gonna look something like that and what about in the x-direction well it looks like in the x-direction right over here is very similar to that one so it might look something like this I'll draw it slightly higher just so you could see it but once again the velocity the x-direction stays the same because in all three scenarios you have zero acceleration in the X direction now last but not least let's think about position so they all start in the exact same place at both the X and Y dimension but as we see they all have different initial velocities at least in the Y dimension so let's start with the salmon-colored one so the salmon-colored one it starts off with a some type of positive Y position maybe based on the height of where the individual's hand is and then what's going to happen well it's going to have positive but decreasing velocity up until this point at this point its velocity is zero so it's position is going to go up but at ever decreasing rates until you get right to that point right over there and then we see the velocity starts becoming more and more and more and more negative so it would look something like something like that now what would be the x position of this first scenario well if we make this position right over here zero then we would have we would start our x position would start over here and since we have a constant positive X velocity we our exposition would just increase at a constant rate it would do something like that now what about this blue scenario well this blue scenario we are starting in the exact same place as in our pink scenario and then our initial y velocity is zero and then it just gets more and more and more and more negative so it would look something it would look something like this now what about the X position well our x position we had a slightly higher velocity at least the way that I drew it over here so we our x position would increase at a concert rate and it would be a slightly higher constant rate so it'd have a slightly higher slope than we saw for the pink one now the yellow scenario once again we're starting in the exact same place and here we're already starting with a negative velocity it's only gonna get more and more and more negative so it's just gonna do something like this it's gonna get more and more and more and more negative it's a little bit hard to see but it would do something like that and if the in the x-direction our our velocity is roughly the same as the blue scenario that our X position over time for the yellow one it's gonna look pretty pretty similar so this is just a way to visualize how things would behave in terms of position velocity and acceleration in the Y and X directions and to appreciate whan how to draw and visualize these graphs and conceptualize them but also to appreciate that you can treat once you break your initial velocity vectors down you can treat the different dimension the X and the y dimensions independently