Problem #$1$: Warning Sign Advance Placement $(20$ points$)$

a$.)$ A lane merge warning sign $($shown below$)$ is being installed near an entrance ramp on a freeway with operating speeds of $80mph.$ Calculate the appropriate advance placement distance $($to the nearest foot$)$ for the sign assuming a perception$-$reaction time of $14$ seconds for the vehicle avoidance maneuver.

b$.)$ A curve or turn warning sign is to be installed near a single curve with a $28mph$ design speed $($per ball$-$bank indicator$)$ on a rural $2-$lane roadway. The prevailing speed of traffic on the approaching tangent section is $62mph.$ Calculate the advance placement distance upstream of the curve PC for this sign $($to the nearest foot$).$ Also indicate the appropriate sign to be used $($curve or turn$)$ and the appropriate safe advisory speed if one is to be posted for this curve.