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$3.$ Drivers must slow down from $65mph$ to $45mph$ to negotiate a severe horizontal curve on a rural highway. A warning sign for the curve is clearly visible for a distance of $120$ feet $($i$.$e$.$ distance the driver can interpret the sign in advance of where the sign is placed$).$ How far in advance of the curve must the sign be located to ensure that vehicles have sufficient distance to decelerate safely? Use the recommended ASSHTO deceleration and a $2$ seconds for the perception$-$reaction times.

$*$Hint: You have to provide a sufficient distance for the vehicle to reach the $45mph$ before the curve. So$,$ assume that the driver will start slowing down once he sees the sign.