Solve the problem.The amount of energy collected by a solar panel depends on the intensity of the sun's rays and the area of the panel. Let the vector I represent the intensity, in watts per square centimeter, having the direction of the sun's rays. Let the vector A represent the area, in square centimeters, whose direction is the orientation of a solar panel. See the figure. The total number of watts collected by the panel is given by  Suppose I =  and A = 

style="vertical-align: -4.0px;" />. (i) Find  and and interpret the meaning of each; (ii) Compute W and interpret its meaning; (iii) If the solar panel is to collect the maximum number of watts, what must be true about I and A? 



A. (i) = 0.081; the intensity of the sun's rays is approximately 0.081 W/cm².  = 583; the area of the solar panel is approximately 583 cm².
(ii) W = 47; 47 watts of energy is collected. 
(iii) Vectors  I and A should be parallel with the solar panels facing the sun.
B. (i) = 0.057; the intensity of the sun's rays is approximately 0.057 W/cm².  = 400; the area of the solar panel is approximately 400 cm².
(ii) W = 47; 47 watts of energy is collected. 
(iii) Vectors  I and A should be orthogonal with the solar panels at a 45° angle to the sun.
C. (i) = 0.081; the intensity of the sun's rays is approximately 0.081 W/cm².  = 583; the area of the solar panel is approximately 583 cm².
(ii) W = 41; 41 watts of energy is collected. 
(iii) Vectors  I and A should be parallel with the solar panels facing the sun.
D. (i) = 0.007; the intensity of the sun's rays is approximately 0.007 W/cm².  = 340,000; the area of the solar panel is approximately 340,000 cm².
(ii) W = 41; 41 watts of energy is collected. 
(iii) Vectors  I and A should be perpendicular with the solar panels at a 90° angle to the sun.

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Answer: C

Mathematics