A construction area exists on an $80k\frac{m}{h}$ design speed highway. How far from this construction spot should the designer put a warning sign so that the drivers can completely stop $30m$ before reaching it$?$ The highway has a downgrade of $3\%.$ Assume that the driver can see the warning sign $50m$ before the sign and carry out the analysis according to the AASHTO method. Assume the driver perceives and reacts to stop the vehicle as soon as they are able to see the sign. Assume the deceleration rate of the vehicle is $3\mathrm{.}4\frac{m}{s}2.$ Assume a standard perception$-$reaction time as per AASHTO.