16 - Light placed above the center of circular area

Problem 16
A light is to be placed above the center of a circular area of radius a. What height gives the best illumination on a circular walk surrounding the area? (When light from a point source strikes a surface obliquely, the intensity of illumination is
 

$I = \dfrac{k\sin \theta}{d^2}$

 

where $\theta$ is the angle of incidence and $d$ the distance from the source.)
 

15-16 Movement of shadow from light at eye level

Problem 15
A light at eye level stands 20 ft from a house and 15 ft from the path leading from the house to the street. A man walks along the path at 6 ft per sec. How fast does his shadow move along the wall when he is 5 ft from the house?
 

Problem 16
In Problem 15, when the man is 5 ft from the house, find the time-rate of change of that portion of his shadow which lies on the ground.
 

43 - 45 Solved problems in maxima and minima

Problem 43
A ship lies 6 miles from shore, and opposite a point 10 miles farther along the shore another ship lies 18 miles offshore. A boat from the first ship is to land a passenger and then proceed to the other ship. What is the least distance the boat can travel?
 

Problem 44
Two posts, one 8 feet high and the other 12 feet high, stand 15 ft apart. They are to be supported by wires attached to a single stake at ground level. The wires running to the tops of the posts. Where should the stake be placed, to use the least amount of wire?
 

Problem 45
A ray of light travels, as in Fig. 39, from A to B via the point P on the mirror CD. Prove that the length (AP + PB) will be a minimum if and only if α = β.
 

06 Review Problem - Area illuminated by light placed in front of the globe Jhun Vert Sun, 05/03/2020 - 06:23 pm

Problem 6
A light is placed 5 ft. from the center of the globe 3 ft. in diameter. Find the area of the illuminated portion.