1484
« 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!
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