Consider the motion of a particle of mass m that starts from rest in a constant grav- itational field. If an air drag force force proportional to the square of the speed (i.e., cu², same as problem 1) is encountered, (a) write and characterize the differential equation describing the motion. (b) find the terminal speed Vterm.. (c) find the distance that the particle falls when its final speed is vƒ, where < Uterm

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter10: Motion In A Noninertial Reference Frame
Section: Chapter Questions
Problem 10.13P
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Two dimensional motion with air drag (think golf ball trajectory) is not integrable, but purely horizontal motion and purely vertical motion are separately integrable.

2. Consider the motion of a particle of mass m that starts from rest in a constant grav-
itational field. If an air drag force force proportional to the square of the speed (i.e.,
cv², same as problem 1) is encountered,
(a) write and characterize the differential equation describing the motion.
(b) find the terminal speed Vterm….
(c) find the distance that the particle falls when its final speed is vƒ,
where
Vƒ
< Vterm.
Transcribed Image Text:2. Consider the motion of a particle of mass m that starts from rest in a constant grav- itational field. If an air drag force force proportional to the square of the speed (i.e., cv², same as problem 1) is encountered, (a) write and characterize the differential equation describing the motion. (b) find the terminal speed Vterm…. (c) find the distance that the particle falls when its final speed is vƒ, where Vƒ < Vterm.
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