Author Topic: Calculus with Velocities and other stuff  (Read 5554 times)

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Offline pimathbrainiac

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Calculus with Velocities and other stuff
« on: January 20, 2013, 03:58:59 pm »
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!
I am Bach.

Offline ruler501

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Re: Calculus with Velocities and other stuff
« Reply #1 on: January 20, 2013, 04:01:16 pm »
why do you go from V(x) to dx^2/dt^2 shouldn't it be dx/dt instead?
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Offline pimathbrainiac

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Re: Calculus with Velocities and other stuff
« Reply #2 on: January 20, 2013, 04:02:14 pm »
V(x) is squared... Did I not put that in?
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Offline ruler501

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Re: Calculus with Velocities and other stuff
« Reply #3 on: January 20, 2013, 04:06:44 pm »
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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Offline pimathbrainiac

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Re: Calculus with Velocities and other stuff
« Reply #4 on: January 20, 2013, 04:07:25 pm »
abs(V(x))^2 is the same as V(x)^2
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Offline ruler501

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Re: Calculus with Velocities and other stuff
« Reply #5 on: January 20, 2013, 04:10:47 pm »
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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Offline pimathbrainiac

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Re: Calculus with Velocities and other stuff
« Reply #6 on: January 20, 2013, 04:12:19 pm »
They're constants... I should have called them c and k, but the way I used is the way the problem is stated
« Last Edit: January 20, 2013, 04:12:33 pm by pimathbrainiac »
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Offline ruler501

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Re: Calculus with Velocities and other stuff
« Reply #7 on: January 20, 2013, 04:14:29 pm »
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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Offline pimathbrainiac

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Re: Calculus with Velocities and other stuff
« Reply #8 on: January 20, 2013, 04:16:13 pm »
But shouldn't there be something done to the X in the exponent?
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Offline ruler501

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Re: Calculus with Velocities and other stuff
« Reply #9 on: January 20, 2013, 04:17:20 pm »
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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PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y

Offline pimathbrainiac

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Re: Calculus with Velocities and other stuff
« Reply #10 on: January 20, 2013, 04:19:52 pm »
I know that is wrong though because when I plug numbers back in, I don't get the right result
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Offline ruler501

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Re: Calculus with Velocities and other stuff
« Reply #11 on: January 20, 2013, 04:24:25 pm »
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
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-----BEGIN GEEK CODE BLOCK-----
Version: 3.1
GCM/CS/M/S d- s++: a---- C++ UL++ P+ L++ E---- W++ N o? K- w-- o? !M V?
PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y