A commander fires a shell at certain angle of projection from ‘A’ which clears the building (cuboid) of dimensions  $20\times 15\times 12.5m^3$  in its diagonal plane. Shell just clears the roof diagonally at points P and Q and falls on the other side of the building at B, and makes  ${45}^0$  angle with horizontal at P and Q as shown in the figure. If the range AB of the shell is  $N\times \sqrt{3}$  metre then find $\frac{N}{5}$. $(g=10m/s^2)$  .