To determine the distance of the focus from the base of the parabolic tunnel, we can use the properties of a parabola. In a vertical parabolic shape, the focus lies on the axis of symmetry, which is parallel to the y-axis. The equation for a parabola with vertical axis of symmetry is of the form x = a(y - k)^2 + h, where (h, k) is the vertex of the parabola.
Given that the maximum height of the tunnel is 5 meters and the base points are 8 meters apart, we can find the equation of the parabola. The vertex form of the parabolic equation is x = a(y - k)^2 + h, where (h, k) is the vertex. Since the vertex is at the maximum height, the vertex is (0, 5).
With the vertex and a point (8, 0) on the parabola (as the base points are 8 meters apart), we can find the equation of the parabola. Plugging the values into the vertex form, we get x = 1/5y^2 + 5.
The focus of the parabola is located a distance of 1/4a units above the vertex. In this case, a = 1/5, so the focus is 1/4(1/5) = 1/20 units above the vertex.
Therefore, the focus of the parabolic tunnel is located 1/20 units above the vertex, which is at a distance of 1/20 * 5 = 1/4 meters above the vertex, and hence, the focus is 1/4 meters above the vertex, or 1/4 meters above the maximum height of the tunnel.
