# 1. A picture of a solar tower is shown below (figure 1). You can see that…

1. A picture of a solar tower is shown below (figure 1). You can see that there are plenty of mirrors located in different positions. Each of these mirrors tracks the sun over time and project the sunlight to the tower. The tower gets very hot and the heat is used to generate electricity (or to evaporate water). To make this problem easier for you, I changed this problem to a 2D example. 4 Figure 1 Solar Tower Figure 2 demonstrates a 2D case. The yellow line is the location of the sun over time, the mirror is located at the position [x,y]tower = [0,400] (meter). The mirror is locate at (x,y)mirror = [7000,0] (meter). The angle ß between the vector connecting the origin to the sun and the positive x axis is described with (it is assumed that sun rises from the positive x axis) B=2*pi/24*60*60*t where t is the time of the day (reported in second) t=0:60:12*60*60 We assume that we have sunlight for 12 hours during the period of t = [0 12*60*60 (sec). It is assumed that sun moves in a circle around the origin with the radius of 10,000 meter. The x and y location of sun at any time can be found as x = r cos(B) z=rsin() 10000 8000 Y (meter) 2000 this is the towefnis is the mirror 0.5 -0.5 0 X (meter) Figure 2 2D Problem *104 a) Your task is to find the angle o between the tilted mirror and the ground (see figure 3) so the sunlight is projected to the tower. You need to report the angle o every minute. Please consider that can be negative. The work done in HW 2 can help you solve this question. I copied the question in hw 2 with the solution here (see figure 3). Solution: 0 = 90 – atº. I also provided a code (see figure 4) that can help you a little with solving this problem. The e needs to be reported at every minute. b) Plot 0 over time. + c) Make an animation that shows the array of sunlight, the mirror (you can show the mirror with a line), and the array of sun reflected from mirror to the tower Figure 34 clc clear hold on box on r = 10000; t = 0:60:12*60*60; f time (reported in minutes) beta = 2*pi/ (24*60*60) *t; % angle of the sun with horizon (reported in minutes) x = r*cos (beta); % The x location of the sun y = r*sin (beta); % The y location of the sun plot (x, y, ‘yo’) plot(0,400, ‘d’) % tower location text (-2500, 800, ‘this is the tower’) plot (7000, 0, ‘bd’); f mirror location text (5000,400, ‘this is the mirror’) xlabel (‘X (meter)’) ylabel (‘Y (meter)’) Figure 4 A Code to Help You