function trajectory(start, target, speed, gPrime)
    local dv = target - start;
    -- displacement
    local dx, dy, dz = dv.x, dv.y, dv.z;
    -- horizontal displacement
    local alpha, beta = sqrt(dx*dx+dz*dz), dy;
    local f = 2*speed*speed / g;
    -- discriminant
    local d = f*(f - 2*beta) - 2*alpha*alpha;
    if d<0 then
        print "can't hit target";
        return nil;
    else
        local root = sqrt(d);
        local gamma0, gamma1 = (f+root)/2, (f-root)/2;
        local theta0, theta1 = atan2(gamma0, alpha), atan2(gamma1, alpha);
        return  theta0, Vector3.new(dx/alpha*cos(theta0), sin(theta0), dz/alpha*cos(theta0))*speed,
                Vector3.new(dx/alpha*cos(theta1), sin(theta1), dz/alpha*cos(theta1))*speed;
    end
end