In this question 1st, were asked about T equals two. Well if I look at the diagram for T equals two and I'm zooming in right now, I would say that tha tha is about three. a quarter. So when T equals two. Datas about equal to three 0.25 radiance. Okay, estimate the coordinates of P. When T. two. Okay. Well this is not a great way of doing this because Uh huh. There's a big difference between 3.1 and 3.2 and 3.3 when you're talking about radiance um interesting but I guess I'm going to go with 3.25 like I said before. So now we've got to estimate the coordinates of P. So we're on a unit circle going to hear Is 3.14. So we're a little bit beyond um So 3.25 -3.14 Because that's pie Uh is zero wow 11 All right, so The sine of 0.11 radiance Which would be the Y. Value at this point um Would be -0.11. Yeah it's negative. Okay. The co sign my goodness Of 0.11. Yeah is negative. 0.9 nine. All right. That looks good. So now we're asked in part B uh when tea is too which we had before we're trying to figure out the speed of point P. In the X. Direction and the speed of point P. In the Y. Direction. Okay so the X coordinate is the co sign of basically tha tha so driven of the coastline is the opposite of the sign. Um Whoops. He said dx over D. T. Uh D theta over D. T. Now Um fate is about 3.25. So negative sign 3.25 D. Theta over DT we can get that from the slope of the graph. D theta over DT when tea is too. So I am looking at the graph and trying to figure out the slope. It looks to me like if we were to draw a line the data there if we were to draw a line through the graph tangent at two then Um it would go from let's say one 23 uh seconds I believe. I'm not sure if we're ever told exactly the units there. Um So from 1 to 3 I would say That it goes to five and maybe 1 1/2. So the tha tha would go from 1.5. 25 So 5 -2. Okay 5 -1 would be 3.5 over to Which is 1.75. Yeah. Yeah. Okay so dictator over D. T. is 1.75. All right putting that into a calculator. Mhm. Negative Sign of 3 to 5 As 1.75 negative 0.1 nine is dx over D. T. Okay so let's get why is the sine of theta. Dy over D. T. Is co sign of theta D. Theta over D. T. However it is moving downwards so I'm going to put a negative in front of their um it's clearly the point is moving downward. Um negative co sign of 3.25 D. Theta over D. T. is still 1.75. Let's put that into a calculator. Co sign That's going to give me negative 1.7. Uh That's definitely more than enough significant digits here. Mhm. All right so the reason why my answers differ from the book is because we're just estimating here. And when you're trying to like I said at the beginning, there's a big difference i in radiance between 3.14 and 3.25. Um because that goes from uh huh. Why value of zero to why value of -0.11 and I can't tell from the graph uh exactly what that is. And then I was also estimating the slope. Um So um nevertheless that's how you do it and thank you for watching.
4.5*10^3/9*10^7=4.5/9*10^3*10^7=0.5*10^3*10^7. a^b*a^c=a^(b+c), so 10^3*10^7=10^(3+7)=10^10. 0.5*10^10=5*10^9, since we want to write in scientific notation where the leading number is bigger than one and smaller than 10.
