SOLUTION: A certain planet has a day length of 24 hours. The planet is totally covered in water, except for one small island. At hour 0, the island has 100% light with the planet’s star in

Algebra ->  Functions -> SOLUTION: A certain planet has a day length of 24 hours. The planet is totally covered in water, except for one small island. At hour 0, the island has 100% light with the planet’s star in      Log On


   

Question 1141493: A certain planet has a day length of 24 hours. The planet is totally covered in water, except for one small island. At hour 0, the island has 100% light with the planet’s star in the top of the sky. At hour 12, the island has 0% light and is in total darkness. Write an equation that models the amount of light in the sky on the island in terms of hours passed.
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
The required equation is
    

    P = k%2Asin%28pi%2F2+%2B+24%2At%29,  if -6 <= t <= 6,

    P = 0            ,  if 6 <  t  < 18.


where P is the light's power (in watts) falling to the unit area of the island; 
and "k" is the constant value coefficient of the light energy absorption by the island' surface.


The sine function reflects the fact that the energy flux is proportional to the sine of the angle 
between the normal vector to the island surface and the direction to the star.