A rough inclined plane $B C E$ of height $\left(\frac{25}{6}\right)\, m$ is kept on a rectangular wooden block $A B C D$ of height $10 m$, as shown in the figure. A small block is allowed to slide down from the top $E$ of the inclined plane. The coefficient of kinetic friction between the block and the inclined plane is $\frac{1}{8}$ and the angle of inclination of the inclined plane is $\sin ^{-1}(0.6)$. If the small block finally reaches the ground at a point $F$, then $D F$ will be (Acceleration due to gravity, $g =10 \,ms ^{-2}$ )