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Homework - Ma 116 Calculus II Hw-1(Solutions Due Feb 9 2011...

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Ma 116 - Calculus II Hw-1 (Solutions) Due: Feb 9, 2011 Pledge and Sign : An important component of these written exercises is the quality of your presentation, including: legibility, organization of the solution, and clearly stated reasoning where appropriate. Points will be deducted for sloppy work or insufficient explanations. 1. An object with mass m is dropped from rest at time t = 0. A model for the object’s velocity v at time t , that takes air resistance into account, is given by the differential equation, dv dt + c m v = - g Here g > 0 is the gravitational acceleration and c > 0 is a positive constant associated with the air resistance. Confirm that v = - mg c 1 - e - ct/m is a solution to the differential equation and satisfies v (0) = 0. Evaluate lim t →∞ v and give a physical interpretation of this limit. Now fix t and evaluate the limit lim c 0 + v . What is the physical interpretation of this limit? Solution : v = - mg c 1 - e - ct/m and dv dt = - ge - ct/m Substitute into left-hand side of the differential equation: dv dt + c m v = - ge - ct/m - g 1 - e - ct/m = - g Solution Confirmed!

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