17-18 A man in a motorboat needs to catch a bus
Problem 17
A man in a motorboat at A receives a message at noon, calling him to B. A bus making 40 miles per hour leaves C, bound for B, at 1:00 PM. If AC = 30 miles, what must be the speed of the boat, to enable the man to catch the bus?
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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
where $\theta$ is the angle of incidence and $d$ the distance from the source.)
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14-15 Ladder reaching the house from the ground outside the wall
Problem 14
A wall 10 ft high is 8 ft from the house. Find the length of the shortest ladder that will reach the house, when one end rests on the ground outside the wall.
13 - Sphere cut into a circular cone
Problem 13
A sphere is cut in the shape of a circular cone. How much of the material can be saved?
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12 - Cone of maximum convex area inscribed in a sphere
Problem 12
Find the altitude of the circular cone of maximum convex surface inscribed a sphere of radius a.
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11 - Triangular gutter of maximum carrying capacity
Problem 11
A gutter having a triangular cross-section is to be made by bending a strip of tin in the middle. Find the angle between the sides when the carrying capacity is to a maximum.
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10 - Largest conical tent of given slant height
Problem 10
Find the largest conical tent that can be constructed having a given slant height.
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06-09 Trapezoidal gutter of greatest capacity
Problem 06
A trapezoidal gutter is to be made, from a strip of metal 22 inches wide by bending up the edges. If the base is 14 inches wide, what width across the top gives the greatest carrying capacity.
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04-05 Stiffness and strength of timber beam
Problem 4
The stiffness of a rectangular beam is proportional to the breadth and the cube of the depth. Find the shape of the stiffest beam that can be cut from a log of a given size.
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03 - Heaviest cylinder that can be made from a shot
Problem 3
Find the weight of the heaviest circular cylinder can be cut from a 16-lb shot.
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