Welcome back, everyone, hopefully had a chance to work this problem now on your own. So we're told this problem that is spacecraft with a reflective sail like material may actually eventually used for low cost space travel. This is a real technology that's actually being used. Um And the science is sound. So we're told that a 400 kg satellite near earth is equipped with these super reflective sails. So I kind of want to draw this out here. And basically what happens is those sails are gonna capture sunlight from the sun and it's gonna generate a radiation pressure. So let me just draw this out here. So you got the sun like this. Uh sorry about my sun. And then at some distance where the earth is, you're gonna have this satellite over here, the satellite like this and this satellite has these big big reflective sails like this. So what happens is the sunlight that travels is gonna hit those reflective sails and it's eventually going to push them to the right. So this is gonna be an f from radiation pressure. All right. So eventually what happens is that, that that object, that satellite is gonna pick up speed and that's actually one way that we could generate large amounts of velocity for spacecraft with very little fuel. You're only just using the light from the sun. All right. So let's take a look here. The area of each of these reflective sails is 5000 m squared. So, in other words, the area is equal to 5000. Uh but actually what happens is the total amount of area is going to be twice of 5000 because there's two of them. So there's two of them uh each are completely, all right. So this area total is gonna equal 10,000. And also we know that we're dealing with completely reflective sales, which means we're gonna be using our reflective radiation pressure equations and not our absorbing radiation equations. All right. So the intensity of sunlight is approximately 1350. In the words, the eye from the sun is about 1350. So now what we want to do is we want to figure out what is in the first part, what's the force that's calculated? Or what's the first force that's exerted on the satellites? All right. So that's F, so we actually know also what type of F we're dealing with again because we know that it is reflective. So we basically want to figure out what is F reflective. All right. So let's get started here with our equation. Our equation says that F reflected is equal to two times I A over C. All right. So do we have everything we need, we have the intensity, we also have the area and we have C that's just a constant. So in other words, what happens is you get two times the intensity which is 1350 in the area, which area we're gonna use here? We're gonna use 5000 or 10,000. Remember we're gonna use the total area of both of the reflective sales. So that means we're actually gonna use the 10,000. All right. So 10,000 is our total area over here. Then we divide by speed of light three times 10 of the eighth. And when you get, uh when you calculate this, what you're gonna get for F reflect is you're gonna get a force of about 0.09 newtons. So this doesn't seem like a very, very big force. But remember this is a constant 0.09 force that will be pushing this satellite. All right. So now let's take a look at the second part here. That's the first part. The second problem asks us assuming that the satellite starts from rest. Then how is it moving? How fast is it moving after one year? So how fast is it moving? That's actually gonna be a velocity. So we're actually gonna look at this force here and we're gonna see how fast it's moving after a certain amount of time. So hopefully, you folks realize that, that has nothing to do with intensity or radiation pressure or anything like that. That's just straight up kinematics. So what, what's basically asking us here is what is the final after one year? So the delta T is gonna be one year. All right. So let's just look at our kinematics equations. This is a constant force that will be pushing this. So it's gonna be a constant acceleration. All right. So in order to figure out the final uh we have, we need to have the initial plus the acceleration times time. That's the most simple velocity formula um of the kinematics equations, right? So we're really looking for what is the final? Now, let's take a look at what the initial is, right? We're told actually what the initial is because we're assuming that satellite starts from rest. So that basically means that V knot is equal to zero. All right. So now we just need acceleration and time. All right. So how do we figure out the acceleration? Well, we can figure out acceleration because we have the force we have 0.09 newtons. So let's just go over here real quick and figure out the acceleration A is equal to remember just F equals ma uh F is um A is equal to F divided by M. So in other words, we have uh f reflect over mass which is 0.09 divided by the 400 kg mass. And what you should get is you should get a acceleration of 2.25 times 10 to the negative or, and that's gonna be meters per second squared. All right. So now this equation, this calculation, sorry, this acceleration but get plugged into the velocity formula. And now the other thing we have to figure out is what is the time. So in other words, this t is equal to one year. And basically what you could do is you could multiply a bunch of stuff out on your calculator. You can multiply this by 365 days times 24 hours times 60 minutes times 60 seconds. And you can see that all the, the units will cancel. Uh But basically what you should get is three points about 15 or 33 million, 153,600. Um That's, you know, uh you can calculate that out yourself. And let's see. Now we plug this into our equation for V final. You get V finals equal to zero plus and then we have two points 25 times 10 to the minus four and then we have seconds, which is 3 million, 153,000. You have to convert it because you can't plug in years into this formula. You have to have everything in si units and what you should get out of here folks is you should get about um you should get about 7100 m per second. All right. So this is actually your final answer for that second part here. So even though we can see that the force is actually very small, the force is only about 0.09 newtons. After it acts for a long time, you actually can get some pretty significant velocity changes. All right. So this is one of those things where we would send the satellite out and years later it would be traveling super, super fast out of the solar system. Anyway, that's it. For this one. Folks, let me know if you have any questions, I'll see you in the next video.