Question

A temporary diversion has been constructed on a highway of +4% gradient due to major repairs that are being undertaken on a bridge. The maximum speed allowed on the diversion is 10 mi/hr. Determine the minimum distance from the diversion that a road sign shpuld be located informing drivers of the temporary change on the highway. Max allowable speed on highway =70 mi/hr

Letter heigh of road sign = 4"
perception -reaction time =2.5 second
The distance of readability of the roadway sign is ______
a) 120ft
b) 100ft
c) 40ft
d) 200ft

Answer 1

The minimum distance from the diversion that a road sign should be located is approximately 377 ft. This calculation takes into account the perception-reaction time and the distance needed to stop the vehicle at a given speed.

Step-by-step explanation:

To determine the minimum distance from the diversion that a road sign should be located, we need to consider the perception-reaction time and the distance needed to stop the vehicle at a given speed.

First, we need to calculate the perception-reaction distance, which is the distance a vehicle travels during the driver's perception-reaction time. The formula for perception-reaction distance is:

Perception-Reaction Distance = Speed imes Perception-Reaction Time

In this case, the speed is given as 10 mi/hr and the perception-reaction time is given as 2.5 seconds. Converting the speed to ft/s (1 mi/hr = 1.47 ft/s), we get:

Speed = 10 mi/hr imes 1.47 ft/s = 14.7 ft/s

Therefore, the perception-reaction distance is:

Perception-Reaction Distance = 14.7 ft/s imes 2.5 s = 36.75 ft

Next, we need to consider the braking distance, which is the distance a vehicle needs to stop at a given speed. The formula for braking distance is:

Braking Distance = (Speed^2) / (2 imes Deceleration)

In this case, the speed is given as 10 mi/hr (14.7 ft/s) and the deceleration is equal to the gradient of the diversion, which is +4%, or 0.04. Plugging in the values, we get:

Braking Distance = (14.7 ft/s)^2 / (2 imes 0.04) = 340.5375 ft

Finally, to determine the minimum distance from the diversion that a road sign should be located, we add the perception-reaction distance and the braking distance:

Minimum Distance = Perception-Reaction Distance + Braking Distance = 36.75 ft + 340.5375 ft = 377.2875 ft.

Therefore, the minimum distance from the diversion that a road sign should be located is approximately 377 ft.