Register to reply 
Tricky Optimization Problem 
Share this thread: 
#1
Nov2005, 09:32 PM

P: 3

can someone PLEASE help me wit this problem? i will be ETERNALLY GRATEFUL. THANK YOU!!.
A light is suspended at a height "h" above the floor. The illumination at the point P is inversely proportional to the square of the distance from the point P to the light ("r") and directly proportional to the cosine of the angle theta. How far from the floor should the light be to maximize the illumination at the point P? light \ o=theta o \  \ h \ r  \  \ __10M__\ floor P 


#2
Nov2005, 09:34 PM

P: 3

light
\ o=theta o \  \ h  \ r  \  \ __10M__\ floor P 


#3
Nov2005, 09:36 PM

P: 3

thats supposed to be a triangle by the way. sry.



#4
Nov2105, 06:46 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,568

Tricky Optimization Problem
I assume that theta is set so that the light is shining directly at point p.
Okay, let "h" be the height of the light which is, after all, what you want to find. Use the Pythagorean theorem to determine r, the straight line distance from the light to P, in terms of h. Use that, together with the definition of cosine, to find cos(theta) in terms of h. Since " The illumination at the point P is inversely proportional to the square of the distance from the point P to the light ("r") and directly proportional to the cosine of the angle theta" you can now write a formula for illumination entirely in terms of h. Differentiate that with respect to h and set equal to 0. 


Register to reply 
Related Discussions  
My tricky wave problem. ehh its probably not tricky.  Introductory Physics Homework  15  
Optimization problem  Calculus & Beyond Homework  11  
Help! Optimization Problem!  Calculus & Beyond Homework  2  
Optimization Problem  Calculus & Beyond Homework  1  
Optimization problem  General Math  5 