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αν m = mg - cv dt (a) Solve this as a linear equation to show that v = mg (1 - e-ct/m). (b) What is the limiting velocity? (c) Find the distance the object has fallen after t seconds.

αν m = mg - cv dt (a) Solve this as a linear equation to show that v = mg (1 - e-ct/m). (b) What is the limiting velocity? (c) Find the distance the object has fallen after t seconds.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An object with mass ? is dropped from rest and we assume that the air resistance is
proportional to the speed of the object. If ?(?) is the distance dropped after ? seconds,
then the speed is ? = ?′(?) and the acceleration is ? = ?′(?). If ? is the acceleration
due to gravity, then the downward force on the object is ?? − ??, where ? is a positive
constant, and Newton’s Second Law gives

dv m- = mg - cv dt (a) Solve this as a linear equation to show that v = ²(1 - e-ct/m). mg (b) What is the limiting velocity? (c) Find the distance the object has fallen after t seconds.
Transcribed Image Text:dv m- = mg - cv dt (a) Solve this as a linear equation to show that v = ²(1 - e-ct/m). mg (b) What is the limiting velocity? (c) Find the distance the object has fallen after t seconds.
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