 This video is just me trying to explain it later. It's about ramps and how they affect gravity. So initially the first thing we were taught was that we have some sort of crate right here and it's at a 60 degree and you have a you have a ramp that's at a 60 degree angle here and there's gravity constantly pulling downwards let's say for the sake of simplicity it's 10 meters per second squared that's the gravity's acceleration so so what would be the actual rate of acceleration going this way and the answer is is something like the gravity gravity times sine 60 because that's because cosine cosine 60 is how much how much of that gets absorbed and sine is how much is left if that makes sense so if you have if you have one like this at zero degrees and gravity's pulling down pushing pulling downwards although all the force gets absorbed less force would get absorbed this way even even less this way and none at all if your ramp is this way so yeah that's a basic overview of how ramps get absorbed but what I was interested in is that there was a problem that was not worded correctly it was about a skate border and a ramp but the problem said half pipe and half pipe half pipes are curves are curves so how would so how would the rate of change look since since ramps are constant rate of change the rate of change is constant of acceleration the rate of change of acceleration is constant I think it's called jerk so but with a curved surface it's constantly changing so let's do one that's exaggerated so looks like this at every point it has a little every point it changes and that sort of looked like to me it was like a tangent line and that's perfect for derivatives if you have if you have a curved surface or a curve the curved line and you see that there's and you want to know what the tangent line here is you just take the derivative take the function that the derivative pops out and insert this the point that you want and that gives you the tangent line if that makes any sense so what I thought was okay since the tangent line here well it's the same as that it'd be 60 60 degrees but if we modeled it as just no let's do 45 degrees for simplicity but if we just said it was 1x and that would be then in order to get the angle to actually get the angle we would have to insert it into the into inverse tangent that would be risk tangent one that would give you a 45 and if we take sign of that that would give us how much we have left how much the actual actual pole going this way so it's pretty simple so I thought well that should work that should work with curved surfaces if you have a little skateboard here and you're going down a curved surface and let's say this curve surface is just x squared over 2 since just to make it simple because it's derivative it's derivative would just be x then this equation would look like this the sign of the inverse tangent of x that would be and its acceleration let's see it go down like 10 its acceleration is 10 meters per second squared going downwards so how much would it be absorbed if you plug this into like a graph it would show you something like this and as you get farther and farther it approaches one never reaches it and as you said before one would look like this and 0 is like that so if we start at 0 right here then it makes sense it's 0 and it gets faster and faster of course losing its effectiveness but it's getting faster and faster slowly like it starts I don't know how the graph shows you and that sort of makes sense to me because it goes slow here it gets faster here faster faster but at a slower rate and if you're starting out here let's say you're here the skateboard and then it should look like that so so we can multiply this by the acceleration so it would look more like this look more like this it approaches 10 at the start but it doesn't and we say that well actually it should start actually gravity's acceleration is negative 10 sorry so it would actually look sort of like this instead and we're saying that we start at this point in the half pipe let's say that's two meters in starting look really messy sorry for that then we start down then we start down here at two wait no we start here at two so that's it so that's your starting point and you keep going this way ah sorry let me figure this out how it's gonna head because I think I got it I think you probably might get it but I don't know where to put the y-axis okay I got it since you start at two you'd be going to forward in this in this previous graph which would be negative 10 if you had negative 10 right here multiply by negative 10 but since you're going backwards this way this graph would sort of be flipped that makes sense no wait yeah it would look more like that sorry I'm still not sure if this is right I'm pretty sure it is so tell me if you're good at this type of stuff if this is how it's done I might do stuff on projectile motion later because that's what we're learning right now that's all