A skier is descending a mountain whose topography is modeled by the surface $z = 3000 - x^2 - 2y^2$. If the skier is currently at the point $(3, 2, 2983)$ and chooses to ski in a horizontal direction that makes an angle of $\frac{\pi}{3}$ with the direction of steepest descent, what is the rate of change of their elevation with respect to horizontal distance?