Welcome back everyone. So this is kind of a cool problem because it actually has to do with real, real life information, real data here about the wave intensity of sunlight. So we're told that wave intensity also applies to sunlight, which is an electromagnetic wave. Uh We're told that it takes approximately 500 seconds for light from the sun to reach the earth. And the intensity when it reaches earth is 1360 watts per square meters. And we're asked to find what's the total power output or the average power output of our sun? All right. So basically what happens is we're looking for P average, right? So we're looking for P average, we're gonna use our wave intensity equation uh because we're also told some information about that, the wave intensity. All right. So let's go ahead and figure this out here. So I know that my wave intensity, I'm just gonna start off with my equation, I equals P average divided by uh A in which really what happens here is if you sort of model the solar system, what happens is that the sun is going to be in the center like this? So this is gonna be like the sun and it radiates light in all directions equally. And earth as it travels along in its orbit, basically travels around in a circle. So in other words, what happens is that light output from the sun because it radiates in all directions, then the sort of spherical area here. So the surface area is going to be the surface area of just a sphere. So in other words, it's perfectly fine for us to use the surface area four pi R squared over here. So intensity is just going to be P average divided by four pi R squared. And we're still looking for this power output over here, we know what the intensity is. So really what happens is we just have to figure out the other variable in this equation which is to figure out the distance. What is the R value? What is the distance between the sun and the earth? So that's all I need to figure out once I figure that out I can plug it into this equation over here to figure out the power output of the sun. So how do I do that? Well, if you take a look at this problem, the distance is not given to us. And while you could go look at this up in your textbook and look it up online, it's very easy to uh we're, we're basically gonna see a really easy way to sort of solve this because when we, we can relate the distance that the light travels and also the speed of light to get a really sort of quick calculation of the distance between the earth and the sun. All right. So what's this R distance here? You could look it up, but you could also relate it to V equals delta X over delta T. So distance uh sorry displacement over time. So really, in this case, what happens is that displacement is going to be your R value. So it's just really easy to solve sort of solve. But this is pretty straightforward, you just take this equation here and just sort of rearrange and put delta T on the other side. So in other words, uh the V here is actually going to be the V, the speed of light. So in other words, VC equals three times 10 to the eighth. So really R is equal to VC times delta T. So in other words, it's just equal to the speed of light, which is three times 10 to the eighth meters per second. And then you multiply it by 500 seconds, right? So now what happens is the seconds will cancel and you'll end up with an approximate for the distance between the earth and the sun, which is 1.5 times 10 to the uh and this is gonna be I think the 10th. All right. So let's take a look at this. This is gonna be, I'm sorry, this is actually gonna be the 11 1.5 times 10 of the 11. So this if you actually look this up in meters, this is actually very close to what the actual distance between the earth and the sun is on average. So you take this number and you plug it back into this equation over here to figure out the power output of the sun. All right. So really what happens is once we rearrange this equation and we're just gonna bring this down here, we're gonna end up with the power output of the song on average is gonna be the intensity which we already know times. And then this is gonna be four pi times R squared. So this is gonna be 1.5 times 10 to the 11th. You're gonna take that whole number and you have to square that. So don't forget that. So you have to square this on the outside and then you have to multiply it by the intensity which we know is actually just equal to 1360. All right. So really, that's what this calculation ends up being once you rearrange. So the average power output of the sun when you do all these calculations is actually gonna be something like 3.85 times 10 to the 26 in watts. And if you actually look this N up for the power output of the sun, this is actually going to be very close to the real number over here. All right. So that's actually how we can take some real information and real data to figure out how much power our, our sun actually produces. And remember this is the amount of energy produces every single second. So it's an insane amount of power. Anyway, thanks for watching. Hopefully this made sense. Let's move on.