006 Review Problem - Area illuminated by light placed in front of the globe
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.
light
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.)
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35-36 Time Rates: Lengthening of shadow and movement of its tip in 3D space
Problem 35
An arc light hangs at the height of 30 ft above the center of a street 60 ft wide. A man 6 ft tall walks along the sidewalk at the rate of 4 ft/sec. How fast is his shadow lengthening when he is 40 ft up the street?
17-18 Rate of shadow in the wall of a building
Problem 17
A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the building.
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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?
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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?
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