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 instantancous 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) = vy. (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 instantancous 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) = vy. (c) Determine the terminal velocity of the mass.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 instantancous 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) = v0.
(c) Determine the terminal velocity of the mass.
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