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.

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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.
%3D
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. %3D
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