$($a$)$ A small aircraft has a total mass of $4000$ kg $.$ the wings are aerofoils with a chord of $2$ meters and an aspect ratio of $10.$ If the lift coefficient of wings is $0\mathrm{.}45$ at the take$-$off settings, determine:

$($i$)$ The take$-$off speed of this aircraft at sea level at standard atmospheric conditions. $(7$ Marks$)$

$($ii$)$ The wing loading. $(2$ Marks$)$

$($iii$)$ The required power to maintain a constant cruising speed of $\backslash (360\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ for a cruising drag coefficient of $0\mathrm{.}035.(4$ Marks$)$

$($b$)$ A circular sign has a diameter of $50$ cm and it is subject to normal winds up to $\backslash (150\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ at $\backslash (10\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $100$ kPa $.$ Determine the drag force acting on the sign. Also, determine the bending moment at the bottom of its pole whose height from the ground to the bottom of the sign is $1\mathrm{.}5$ m $.$ Disregard the drag on the pole $17$ marks$)$