13. Establish a coordinate system as shown in the figure, and the equation of the parabola can be set as $x^{2}=-2 p y, M\left(p,-\frac{p}{2}\right)$, then
$$
A\left(0.8,-\left(\frac{p}{2}-3\right)\right) \text {. }
$$

Thus, $0.8^{2}=-2 p \cdot\left[-\left(\frac{p}{2}-3\right)\right], p^{2}-6 p-0.64=0$, the width of the arch opening is at least $2 p=6+\sqrt{38.56} \approx 12.21$.
13. A truck is 3 meters high and 1.6 meters wide, and it needs to pass through a parabolic tunnel, where the arch opening width is exactly the length of the latus rectum of the parabola (a line segment $p_{1} p_{2}$ formed by a line perpendicular to the axis of symmetry of the parabola, intersecting the parabola at points $p_{1}$ and $p_{2}$, is called the latus rectum). To ensure that the truck can pass through the tunnel, what is the minimum width of the arch opening in meters?