Let v(t) be the velocity of an object of mass m in free fall near the earths surface If we assume that air resistance is proportional to v 2 , then v satisfies the differential equation m dv dt g kv 2 for some constant k 0 (a) Set a (g k) 2 and rewrite the differential equation as k m dv dt (a v) T...

a Let a gk 2 Then dv dt Separating variables and integrating yields Therefore 11 k k 12 1 m k ...

Let v(t) be the velocity of an object of mass m in free-fall near the earths surface.

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Let v(t) be the velocity of an object of mass m in free-fall near the earth’s surface. If we assume that air resistance is proportional to v², then v satisfies the differential equation m dv/dt = −g + kv²for some constant k > 0.

(a) Set a = (g/k)/2 and rewrite the differential equation as k m dv dt (a-v) Then solve using Separation of

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 12, 2023 11:37 PM

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Let v(t) be the velocity of an object of mass m in free-fall near the earths surface.

Question:

(a) Set a = (g/k)¹/2 and rewrite the differential equation as k m dv dt (a²-v²) Then solve using Separation of Variables with initial condition v(0) = 0. (b) Show that the terminal velocity lim v(t) is equal to -a. 1-00

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a Let a gk 2 Then dv dt Separating variables and integrating yields Therefore 11 k k 12 1 m k ...View the full answer

Calculus

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