Omnimaga
General Discussion => Other Discussions => Math and Science => Topic started by: pimathbrainiac on January 20, 2013, 03:58:59 pm
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So I have a system of equations:
Variables:
V(x) - x velocity
V(y) - y velocity
C(x) - x constant
C(y) - y constant
t - time
g - gravity constant
dx, dy, dt, dV(x), dV(y), etc. - you can guess what these are
Problem:
dV(x) = C(x)*V(x)^(2)*dt
dV(y) = (C(y)*V(x)^(2)+g)*dt
dt = dy/V(y) = dx/V(x)
solve for V(x) and V(y) in terms of x and y
What I've done so far:
dV(x) = C(x)*(dx^2/dt^2)*dt
dV(x) = C(x)*V(x)*dx
Vx^(-1)*dV(x) = C(x)*dx
Integrate both sides (c is assumed to be 0 here) to get
ln(abs(V(x))) = x*C(x)
e^(x*C(x)) = abs(V(x))
good so far, right?
I sub in e^(x*C(x)) for V(x) in the next equation
dV(y) = (C(y)*e^(2*x*C(x))+g)*dt
dV(y) = (C(y)*e^(2*x*C(x))+g)*(dy/V(y))
V(y)*dV(y) = (C(y)*e^(2*x*C(x))+g)*dy
Now I'm stuck because I don't know how to integrate this equation
Help, please!
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why do you go from V(x) to dx^2/dt^2 shouldn't it be dx/dt instead?
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V(x) is squared... Did I not put that in?
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V(x) is squared... Did I not put that in?
You did just I'm not paying attention.
One other note is that you go from abs(V(x)) to V(x). I'm not sure if that would be considered a safe assumption
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abs(V(x))^2 is the same as V(x)^2
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abs(V(x))^2 is the same as V(x)^2
Ok just how you wrote it up its not obvious thats your reasoning. It just says e^(x*C(x)) = abs(V(x))
good so far, right?
I sub in e^(x*C(x)) for V(x) in the next equation
Is C(y) and C(x) constants or are they functions that can have different outputs depending on the x and y?
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They're constants... I should have called them c and k, but the way I used is the way the problem is stated
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then you have a constant your integrating(relative to changes in y) so you have 1/2V(y)^2=y*(C(y)*e^(2*x*C(x))+g)
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But shouldn't there be something done to the X in the exponent?
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But shouldn't there be something done to the X in the exponent?
why? your integrating relative to dy not x. assuming x and y are independent then there should be nothing done to the x
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I know that is wrong though because when I plug numbers back in, I don't get the right result
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I think the problem may be in your first integral, but I'm not sure where. Try plugging in the values from it back to the original equations and see if thats working