Answer: the distance in advance of the curve the sign must be located to ensure that vehicles have sufficient distance to decelerate safely is 292.07 ft
Step-by-step explanation:
first we calculate the distance to place sign board in advance to curve for decelerating the speed
d = 1.47Si t + [ (Si² - Sf²) / 30(0.348 ± 0.01G)
where d is the safe stopping distance, initial speed is Si (60 mi/hr ), time reaction is t (2.5s), Sf is the final speed (40 mi/hr), G is the grade (0).
so we substitute
d = (1.47 × 60 × 2.5) + [ (60² - 40²) / 30(0.348 ± 0)
= 220.5 + ( 2000/10.44)
= 220.5 + 191.57
= 412.07 ft
Now giving that a warning sign is clearly visible at a distance of 120 ft
optimum safe distance will be
d = minimum distance - sign visible distance
d = 412.07 - 120
d = 292.07 ft
therefore the distance in advance of the curve the sign must be located to ensure that vehicles have sufficient distance to decelerate safely is 292.07 ft