(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.
(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.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 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.
Expert Solution
Step 1
Differential equation model for the velocity of a falling mass m where air resistance is proportional to the instantaneous velocity of the mass, is given by
We can solve the differential equation either by variable separable method or by linear equation method.
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