anonymous
  • anonymous
Why doesn't my integration work out?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
dumbcow
  • dumbcow
because its lazy ...
Luigi0210
  • Luigi0210
I like Pi
anonymous
  • anonymous
I have this differential equation: |dw:1370986567830:dw| With the conditions when t=0, s=0 and v=30 I can't get a valid constant!! please help! <3

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anonymous
  • anonymous
@dumbcow thank you, so insightful :)
dumbcow
  • dumbcow
haha anyway what does g represent? are these v(t) and s(t) functions ?
dumbcow
  • dumbcow
ok well i assumed "g" is a constant and solved diff equ for v(s) \[\large v(s) = \sqrt{15g-ke^{-2s/15}}\] using initial values, s=0 v=30 i solved for constant of integration \[k = 15g -900\] hope that helps
anonymous
  • anonymous
sorry had to log straight after asking the question, g is gravity, v is velocity and s displacement - i separated the variables to get this |dw:1370994064170:dw| and need to solve for S x
dumbcow
  • dumbcow
you can integrate left side using substitution let u = 15g - v^2 du = -2v dv \[\rightarrow -\frac{15}{2} \int\limits \frac{du}{u} = \int\limits ds\]
anonymous
  • anonymous
ah yeah i tried that i got: \[-15/2 \int\limits_{}\frac{ -2v }{ 15g-v^2 }{} = \int\limits_{}ds{}\]
anonymous
  • anonymous
and then
anonymous
  • anonymous
\[-7.5 (\ln15g-v^2) = s+C\]
anonymous
  • anonymous
Using conditions s=0 v=30
anonymous
  • anonymous
\[-7.5 \ln(147-900) = C\]
anonymous
  • anonymous
not valid?
Jhannybean
  • Jhannybean
Oh...all along i was thinking "g" was another function :\ Oops!
anonymous
  • anonymous
no worries! i didnt explain it properly was short of time
dumbcow
  • dumbcow
did you see my earlier post ... before you find constant you need to solve for v
Jhannybean
  • Jhannybean
@KateLovesPie are you in class right now or taking a test? Just wondering.
anonymous
  • anonymous
no lol neither
anonymous
  • anonymous
@dumbcow please could u show how u got to that?
dumbcow
  • dumbcow
sure, just to clarify what is it you are trying to solve in the end?
anonymous
  • anonymous
i need an expression for S :)
dumbcow
  • dumbcow
oh ok i was solving for V
anonymous
  • anonymous
ah i see ok yeah i was almost there with the ln above but it's not valid for C
dumbcow
  • dumbcow
hmm i think i know where you went wrong...since we want expression for s or s(v) you will include constant on right side NOT left side, it may affect the sign \[-7.5\ln(15g-v^{2}) +C = s\] then s=0 , v=30 \[C = 7.5\ln(15g - 900)\] maybe?
Jhannybean
  • Jhannybean
Good luck with your problem!
anonymous
  • anonymous
thank you! thats looking better, the problem is within the ln function being negative as its ln(-753) :/
dumbcow
  • dumbcow
oh shoot i didn't notice that...yeah thats no good
anonymous
  • anonymous
lol it's a tricky one!! the only way would be if it was ln(v^2-15g) which is what the answer says but i dont understand why this method isn't working out
dumbcow
  • dumbcow
yeah lets see if we can arrange the diff equ differently \[15v \frac{dv}{ds} = -(v^{2} -15g)\] \[15 \int\limits \frac{v}{v^{2} -15g} dv = - \int\limits ds\] \[7.5 \ln(v^{2} -15g)+C = -s\] \[C = -7.5\ln(900-15g)\] yes ? :)
anonymous
  • anonymous
yayy thank you!! seems like the other method should've worked as well which is really confusing! thanks so much for your help :)
dumbcow
  • dumbcow
your welcome reason 1st method didn't work wasn't because math was wrong but just cuz it made function undefined for certain values of "v"
anonymous
  • anonymous
Good work. Are you in an elementary differential equations class @KateLovesPie? This seems like an air resistance problem.
anonymous
  • anonymous
ah i see, i was sure i must have gone wrong somewhere, that makes more sense now :D
anonymous
  • anonymous
it is actually :) and i'm doing a level further maths, its part of the mechanics option, exam next week o.o
anonymous
  • anonymous
@oldrin.bataku do the signs normally switch with air resistance problems?

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