Newton's Second Law of Motion

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February 6, 2013 - 8:11am
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Reynan Cabido's picture
Reynan Cabido
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Newton's Second Law of Motion

A body falls from rest. If the resistance of the air is proportional to the speed, and if the limiting speed is 160ft/s, find the speed at the end of 5 seconds.

thank you po..

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February 6, 2013 - 2:33pm
Romel Verterra's picture
Romel Verterra
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Re: Newton's Second Law of Motion

Net force = weight - resistance
$ m\dfrac{dv}{dt} = 9.81m - kv $

$ m\dfrac{dv}{9.81m - kv} = dt $
 

Integrate both sides
$ t = -\dfrac{m}{k}\ln(9.81m - kv) $
 

Do you have the value of the mass, m? It seems we cannot eliminate m here...

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February 6, 2013 - 2:38pm
Romel Verterra's picture
Romel Verterra
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Re: Newton's Second Law of Motion

For a second thought, I think you can use this equation for this problem...
$ \dfrac{dv}{dt} = -kv $

$ \dfrac{dv}{v} = -k \, dt $

$ \displaystyle \int \dfrac{dv}{v} = -k \, \int dt $

$ \ln v = -kt + \ln C $

$ \ln v = \ln e^{-kt} + \ln C $

$ \ln v = \ln Ce^{-kt} $

$ v = Ce^{-kt} $
 

Update us what you've got, we will appreciate it much.

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