anonymous
  • anonymous
how to solve this ODE: I will post it
Mathematics
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anonymous
  • anonymous
how to solve this ODE: I will post it
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
\[\frac{ d ^{2} x }{ dt } = 32 - \frac{ v^2 }{ 8 }\]
anonymous
  • anonymous
I tried to solve it for v then for x, but it was very messy.
anonymous
  • anonymous
@e.mccormick

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anonymous
  • anonymous
anonymous
  • anonymous
\[\frac{ d }{ dt }\left( \frac{ dx }{ dt } \right)=32-\frac{ v^2 }{ 8 }\] \[\frac{ dv }{ dt }=\frac{ 256-v^2 }{ 8 }\] \[\frac{ dv }{ 256-v^2 }=8 dt\] \[\frac{ dv }{ \left( 16-v \right)\left( 16+v \right) }=8 dt\] \[\left\{ \frac{ 1 }{\left( 16-v \right)\left( 16+16 \right) } +\frac{ 1 }{ \left( 16+16 \right)\left( v+16 \right) }\right\} dv=8dt\] can you solve further?
anonymous
  • anonymous
of course you don't need to make partial fraction as you can sub.with sin theta and you will get ln(sec+tan) +k and then integrate which that!! my text didn't discuss DE at all just basic integral, but he gave that equation and said after 1 minute it will hit the ground, so find height??(ans 555) I am puzzled about what is his simple way to deal with that?
anonymous
  • anonymous
when t=1 sec. when it touches the ground v=0 find the value of constant then again integrate to find x when t=1 x (height)=0 find value of constant.
anonymous
  • anonymous
sorry 1 min. just take t=1
IrishBoy123
  • IrishBoy123
@Catch.me why don't you just scan or link the actual question? the DE is not the problem, it is quite straightforward. sight of the question and the IV's would be interesting. @phi
IrishBoy123
  • IrishBoy123
and, as a complement to @surjithayer 's excellent input: \[\ddot x = \frac{dv}{dt} = \ v \frac{dv}{dx}\] :p
anonymous
  • anonymous
V final can't be zero as it is a different scenario. I solved it, but 60 in expm. worries me. any way thanks guys

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