Airplane Payload Problem: The number of kilograms of payload an airplane can carry

Chapter 15, Problem 10

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Airplane Payload Problem: The number of kilograms of payload an airplane can carry equals the number of kilograms the wings can lift minus the mass of the airplane, minus the mass of the crew and their equipment. Use these facts to write an equation of the payload as a function of the airplanes length. The planes mass is directly proportional to the cube of the planes length. The planes lift is directly proportional to the square of the planes length. a. Assume that a plane of a particular design and length L = 20 m can lift 2000 kg and has a mass of 800 kg. Write an equation for the lift and an equation for the mass as functions of L. b. Assume that the crew and their equipment have a mass of 400 kg. Write the particular equation for P(L), the payload the plane can carry in kilograms. c. Make a table of values of P(L) for each 10 m from 0 to 50 m. d. Function P is cubic and thus has three zeros. Find these three zeros, and explain what each represents in the real world.