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Problem 7.10

12 November, 2015 - 11:22

In free fall, the acceleration will not be exactly constant, due to air resistance. For example, a skydiver does not speed up indefinitely until opening her chute, but rather approaches a certain maxi- mum velocity at which the upward force of air resistance cancels out the force of gravity. If an object is dropped from a height h, and the time it takes to reach the ground is used to measure the acceleration of gravity, g, then the relative error in the result due to air resistance is 1E=\frac{g-g_{vacuum}}{g} =1-\frac{2b}{In^{2}(e^{b}+\sqrt{e^{2b}-1})}where b = h/A, and Ais a constant that depends on the size, shape, and mass of the object, and the density of the air. (For a sphere of mass mand diameter ddropping in air, A= 4.11m/d^{2} . Cf. problem 20, p. 49.) Evaluate the constant and linear terms of the Taylor series for the function E(b).