(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.
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Need help with part C.
Transcribed Image Text:(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
Concept and Principle:
The differential equation that represents the falling object is,
Integrating we get,
From part (b) we arrive at the terminal velocity equation,
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