 So this is when we have a ball Okay, let's say the ball is traveling in this direction and it's traveling at Let's use simple numbers 10 meter oops 10 meters per second Okay It doesn't have to have Eunice you could just What about it? Then I don't even know what the Z knows I thought this is 10 meters per second. Okay now Assume that there is We want to find the final Velocity of this thing If there is another force, let's say the wind is blowing. So this guy here Was a gigantic ball kicking the ball at a goal post right here's a guy goalie, right and And This guy's Mental calculation is trying to do it because there's wind blowing in this direction Right at let's say two meters per second Okay Where is what's the true direction? Where is this ball going to go because the goalie is going to try to figure out where it's going to go and this guy's Hopefully Compensated for the wind so you can get it in the top corner, right? so you can score a goal, right and They can give balls different types of spins right in Pool billiards we call it English you get up to us and the ball goes like this, right? So what you do is to be able to do this problem you draw your vectors and what you need is an angle, right? Let's assume. This is at 40 degrees and let's assume this guy is at 15 degrees okay So you draw your vectors you go this is 40 and This will not 40 this guy is 10 right 10 going off the horizontal at 40 degrees and over here you have The wind affecting this guy and the wind is to and it's going on off the horizontal at 15 degrees Okay, let me draw these bigger. So you see them a little bit Usually you try to make the vectors Relative like if this is 10 to is going to be smaller, right? You wouldn't make the two really big So this guy's two and the angle is 15 degrees, right? So for you the only way to be able to do this you have to break these things down to their XY axis coordinates Right, so what you end up doing is you draw here. Let's put our axes here You draw your x-axis you draw your y-axis and what you want to do I'm gonna bring a different color in here now Let's bring a different color. Let's bring green. How's the green? This is really easy. Yeah, that should work. Cool So what we want to do is we want to figure out what the y component of this is and what the x component of that is Right, and this ends up being just straight-up geometry Right so cotoa Right, so this is your x for the ball. Let's call it xb and yb or b x and b y That's a better way of putting it b x and b y So this is b x and b y the x component of the ball and the y component of the ball I can really understand the concept of the reflection using vectors Can you help me with it after you finish? I can really understand the concept of Reflection using vectors can't I can't really understand. I was like what I can't really understand the concept Reflection using vectors. Yeah, we can do it. We finish this as soon as we finish this. Let me know you know, I'll put a little sign here reflections Elections and we'll do okay Mask of Raven I was asking if Riemann hypothesis could be proven using Xenials Paradox I should think I Should link you YouTube from 2018 that may explain better than I can if you can link it up On the discord page that'd be great. That way I can take a look at it too later Sir Michael Atia 89 year-old mathematician claims to have solved the 160 year-old problem really Riemann hypothesis. Check this out. So we want the x component of this. Well the x component of this if you use so cotoa Sine theta is equal to Opposite over hypotenuse Coast data is equal to adjacent She said two to these adjacent Over hypotenuse and tan theta is equal to opposite over adjacent right so Here's our 90-degree triangle This is 40 degrees Opposite over hypotenuse Adjacent over hypotenuse. So if you want to find this out This guy here, we'll do it here and then we're going to raise a whole bunch make us more room, right? Oh That's enough proof wasn't great from what I've heard from other mathematicians. Oh, well, you know that masquerade was cool So this guy becomes close of 40 degrees is Equal to adjacent which is ball in the x direction divided by the hypotenuse, which is 10 So B of x if you cross multiply B of x is equal to 10 Coast 40, right? Let's erase this So B of x is equal to 10 Coast 40 degrees If you use the same thing for sine for this this becomes 10 sine of 40 degrees Never actually looked at it. Did it use Xenos? I gotta look up with Xenos paradoxes, right? So this is the direction that this guy's going the ball This is the direction for the Y component of the ball and then we've got to do the same thing here, right? if we do the same thing here we're gonna get the Wind in the x direction and the wind in the y direction, right? I believe so my information could be wrong Keep in mind. I am still learning and absorbing lots of data once cool fun to do So this guy is the same type of thing that happens over here So this becomes two coasts of 15 to Coasts of 15 and this becomes two sine of 15. So let me put this guy here We'll put a little arrow whoop put it here and Wind in the y direction is two Sine of 15 degrees, right? But here's a kicker Here's a kicker, right? We said that you have to give positive and negative Depending on which direction things are going Right Tyler. Thanks Tyler. I appreciate it. I love it. I love I love doing this, right? So if you're giving positive and negative in certain directions What we're gonna do we're gonna say this way is positive and that way is positive for the Y, right? So this way is positive for the X and that way is positive for the Y and Anything in going in this direction is going to be negative for the X and going down is going to be negative for the Y Well, this is going in this direction. So it's positive for the X. That's going in that direction. So it's positive for the Y That's going in that direction. So that's still positive in the X But this guy is going down the wind Y is going down, right? So this is not two sine of 15. It's negative two sine of 15 negative two sine of 15 So what we end up doing is this now If you want to visualize what's happening, we're taking this vector putting it here right and Then we're taking this part putting it right at the End of it right because they're both going the same direction This part of it is 10 cos 40 degrees this part is too close too Here going up Right, that's 10 sine 40 and then this one is coming down Is going to be negative two sine 15 Okay So what we end up doing now is this focus is there we go what we end up doing now is adding these guys up We're going to get a number. We're going to add these guys up. I'm going to get a number. Let's do that down here Okay So take a look at this. I'm just going to punch in the numbers. I got to do it on the computer So let me punch these in on the computer. You guys can do it as well Right, so we're going to do let's do this one cos of 40 40 cos Times 10 I shouldn't involve so this part here. Let's draw it here This guy is 7.66 we're going to take it to two decimal places 7.66 meters Per second. I should have just said me. Well, you can do it per second All right, and then this part let's figure out what this part is cos 15 times two 15 cos Did I do yeah, I was close cos times two Is 1.93 1.93 Right So this whole thing is these two guys added up, right, which is going to be plus 7.66 7 0.66 Which is 9.59 So let me erase this so it's not confusing So both of those added up is 9.59 9.59 Let's combine this and the wind is giving it more power. Do you know who mr. Gertie is no, I don't I'm not sure if that's directed at me or not Let's do this one This one is going to be 40 sign 40 times 10. So let's take 40 Sign times 10 is going to be six point four three So six point four three six point four three minus Because that's going down 15 sign 15 sign Times two Minus point five two 0.52 so this part here is going to be Minus Six point four three Which is Five point nine one so the total in this direction ends up being which is really going to be here If you're going to look at it with vectors because those two guys kill each other is going to be five point nine one five point nine one Okay, I really struggle with math because I'm dyslexic I struggled with reading because I have a little bit of dyslexia as It comes out when it comes to try to pronounce names and reading things backwards people have noticed when I reach out Sometimes I have to correct me from what I've read right it's just a Little bit of a struggle a little bit more effort from my part That I have to put in and I've taught I've taught people with who have this this actually have some severe some not Granda speak up, please I'm assuming you're not What do you call it? You might be here just to play but just in case just in case you're legit you got math problem because you've got dyslexia Put the effort in I've worked with students that have had that problem and they excel they can't excel So all you got to do now is just do the Pythagorean theorem All right, actually that goes to here. I guess It goes there. It's ASMR and headphones are your friend So cotoa like yeah, it's supposed to be chill. It's supposed to be chill So if we do this try to figure out the magnitude of this thing Which is going to do Pythagorean theorem a squared plus b squared is equal to c squared So it's going to be nine point five nine squared plus Five point nine one squared is equal to c squared. So let's just do that Okay, nine point five nine squared nine point five nine Failed now because of squared. Why did you fail now plus? Five point one one squared equals that 126.90 So this becomes 26.90 is equal to c squared. So c is equal to the square root of that, right? because of what did you say because of Circles I got an eight head up You got an eight Let's check it out square root that I think it should be more in eight. You got eleven point two six 11.26 this that's the magnitude here, right? So the balls traveling faster than this guy kicked it thanks to The wind power, right? Now you could figure out what the angle is as well, right because the angle is going to be Going down now It's going to be less than 40 degrees and the way you figure that out is you're going to use so cotoa again Okay, so the way you do that is let's just use tan, I guess tan theta is equal to Opposite over adjacent which is six point four three divided by 9.59 so theta is equal to tan inverse of that do it whatever that is. Let's do it Could you help me with topics 12.11 of The a-level spectrum modeling with differentials because I'm really strong with them. Oh Harvey I Couldn't help you on that. I haven't done that stuff for a long time Modeling with differential equations or integration and stuff like this at some point I will get back into it and we will definitely hold live streams For it but right now Specifically just focusing on I know brother I know for you know how many people have had that have asked me to teach them calculus And I will at some point, but I can't do it right now It's too much on my plate to for me to go learn relearn calculus 33.84 degrees 33.84 degrees so this angle now is 33.84 Four degrees so the guy kicked it this way the wind is pushing in this way. So the ball is actually going to go According to my diagram this angle the true motion of the angle is 33.84 33.84 degrees and it's going to be traveling at 11.26 meters per second Can we go back and watch your old streams? Yeah, I had I'm just gonna leave this up. So you take a look. I'm just gonna catch up with the chat Dang, yeah Am I on the good or naughty list? I have no idea. I don't have a good and naughty list You're either in my class or you're out. I had that issue in school, too