Brainstorm about the problem 1 and solving labeled diagram of the describe escenario and others

1. By the fourth day of Module 1, make an initial brainstorming post for Task One. This post must be made before you see other student's work and before you actually attempt the problem. A. Brainstorm Post Requirements: After reading the problem, but before making any calculations, you must write out in words your best conjecture of a solution trajectory for the problem. Your solution trajectory must generally describe how you think the problem should be solved, including what calculations you anticipate needing to make and ideas for how to use the results of those calculations to progress toward a solution. You must also include a labeled drawing or diagram of the problem, referencing the quantities that you anticipate being useful in your solution. B. The point of this post is to brainstorm: you're encouraged to give your best guess (even if you end up being way off), to describe what you don't understand about the problem, or even to lay out your current understanding of vectors and then conclude that you're not sure where to start. You will solve the problems together by the end of the module week, so the point is to work together and help and build from each other. 2. By the fifth day of Module 1, post an initial solution to Task One. This should build off your and your peers' brainstorming post, but it is still fine for your initial solution to be incomplete! Problem 1: You have installed a new solar panel on the rootc of your house. We will situate the x-y plane so that the panel runs between the points (0, 3) and (7, 0). We want to know at what times of day the panel will receive the most sunlight. For simplicity, the curve x2 -l- y2 = 81 determines the path from which we will measure the sunlight rays. The following GeoGebra application provides unit vectors that run along the normal lines to this curve at different points. However, you could also use tools from Calculus | to make these vectors {i.e., make normal lines and take unit vectors in the normal direction). These unit vectors represent a single "unit" of sunlight (loosely modeling the notion of sunlight iatensity at varying times of day}. The depicted rotation starts at noon and ends at 8pm. A 10~ Rotation : 25% 0 .. 0.38 0.92 Representative Sun Ray Calculate how much ofa "unit" of sunlight is absorbed by the panel at three different times along the path of the sun (Hint: absorption is modeled by the orientation of the vectors rather than by distances, determine the orientation ofthe sun's rays with respect to the orientation of the panel}. Then determine at what rotah'onls) the solar panel will receive the most "units" of sunlight. You must justify your choice of rotationls}. (Note: You only need to work with the vectors listed in the applet. You can generalize this if you want to, but the problem only requires you to consider the vectors given as the rotation goes from 0 to 100 and to identify which of those vectors maximizes the sunlight "units"). Your solution should include a labeled diagram of the described scenario and include drawn and labeled soluhon vectors. For instance, if a problem requires the creation of a new vector, you must draw that vector. If a problem requires a dot product. you must draw and label the projection vector whose size is being measured