a hockey puck of mass m is sliding in the +x direction across a horizontal ice surface. while sliding, the puck is subject to two forces that oppose its motion: a constant sliding friction force of magnitude f, and a air resistance force of magnitude [tex] cv^2 [/tex] , where c is a constant and v is the puck's velocity. At time t=0, the puck's position is x=0, and it's velocity is [tex] v_{o} [/tex] In terms of the given parameters (m,f,c, and v_o), determine:(adsbygoogle = window.adsbygoogle || []).push({});

a) how far the puck slides, that is determine it's position x when it comes to rest;

for a) i got [tex] F=-(f+cv^2) [/tex]

[tex]m\frac{dv}{dx}\frac{dx}{dt}=-(f+cv^2) [/tex]

[tex] mvdv=-(f+cv^2) [/tex]

[tex] \frac{mvdv}{(f+cv^2)}=-dx [/tex]

takeing the intergral of both sides you get (i think)

[tex] \frac{m}{2c} ln(f+cv^2)=-x [/tex]

[tex] x=-\frac{m}{2c}ln(f+cv^2) [/tex]

now the b) part asks how long does the puck slide, that is, determine the time t at which it comes to rest.

i think i need to turn a [tex] v [/tex] into [tex] \frac{dx}{dt} [/tex]

but i'm not sure where to start or how

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# Homework Help: Hockey puck

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