gistfile1.txt

// x = vx*t
// y = vy*t - 0.5g*t^2
//
// vx = x/t
// vy = (y+0.5g*t^2)/t
//
// vx*vx + vy*vy = v0*v0
//
// v0*v0 = (x/t)^2 + ((y+0.5g*t^2)/t)^2
// v0*v0*t^2 = x^2 + (y+0.5g*t^2)^2
// 
// Let s = t^2
// 
// v0*v0*s = x^2 + (y+0.5g*s)^2
//         = x^2 + y^2 + 2*y*0.5*g*s + 0.25*g^2*s^2
// v0*v0*s = x^2 + y^2 + y*g*s + 1/4*g^2*s^2
// 

A = 0.25*g^2
B = -v0*v0 + y*g
C = x^2 + y^2

// s = (B +- sqrt(B^2-4AC))/2A
// multiple solutions correspond to shooting up or shooting down?
// favor the slower path to avoid negative s, but could use logic
// to test both cases and take faster non-negative case

s = B + sqrt(B^2-4*A*C)/(2*A)
t = sqrt(s)
vx = x/t
vy = (y+0.5*g*t*t)/t
theta = atan2(vy,vx)  // may need to negate one of these
// theta is in radians

// no further expansion of the math is needed since this is going into a 
// computer program, so it can compute A,B,C,s,t,x as above