4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of time. Assume that air resistance is proportional to the instantaneous velocity, with a constant of proportionality k > 0 (this is called the drag coefficient). Take the downward direction to be positive. (b) Solve the differential equation subject to the initial condition v(t = 0) = vo. (c) Determine the terminal velocity of the mass.
4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of time. Assume that air resistance is proportional to the instantaneous velocity, with a constant of proportionality k > 0 (this is called the drag coefficient). Take the downward direction to be positive. (b) Solve the differential equation subject to the initial condition v(t = 0) = vo. (c) Determine the terminal velocity of the mass.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Step 1
Given, mass of the object = m.
Let 'v' be the instantaneous velocity of the object free falling.
Air resistance is assumed proportional to instantaneous velocity as: ; where is the proportionality constant.
(a) Free body diagram of the falling mass is drawn below.
Here, ; where acceleration of the mass,
------------------------------ (1)
Equation (1) represents the differential equation to model velocity (v) of falling mass (m).
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