Sapling Learning As a city planner, you receive complaints from local residents

Question

Sapling Learning As a city planner, you receive complaints from local residents about the safety of nearby roads and streets. complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents com that the speed the (55 too to allow vehicles to stop in time. Under normal itions this is not a problem, but when fog rolis in visibility can reduce to only 155 feet. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.536 and 0.599, whereas the effective coefficient of friction between a skidding (locked Wheel and asphalt ranges between 0.350 and 0.480. Vehicles of all types travel road, from small VW bugs weighing 1310 ib to large trucks weighing 7.50 x 103 lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the miminim and maximum braking distance needed to ensure that all vehicles traveling at the posted speed limit can stop before reaching the intersection Minimum Maximum Number Number 288.93 ft 210.68 Given that the s to allow all vehicles to come safely to a stop before reaching the intersection, calculate the maximum desired speed limit. Number (Soroll down for more questions.) 46.92 mph A Previous check Answer Next HExit O

Explanation / Answer

let friction coefficient be k.

then deceleration=k*g

so if initial speed is v and final speed is 0,

then braking distance=(v^2-0^2)/(2*k*g)

=v^2/(2*k*g)

given v=55 mph=24.5872 m/s

g=9.8 m/s^2

then braking distance=24.5872^2/(2*k*9.8)

=30.8434/k

so minimum braking distance=30.8434/k_max=30.8434/0.599=51.4915 m=168.9353 ft

maximum braking distance=30.8434/k_min=30.8434/0.35=88.124 m=289.12 ft

let desired maximum speed limit be v m/s

then breaking distance=v^2/(2*k*g)

given breaking distance=155 ft=47.244 m

we get=> v=sqrt(2*k*9.8*47.244)

using the minium possible value of k , the speed limit should be

sqrt(2*0.35*9.8*47.244)=18.0026 m/s=40.27 mph

reaction time of the driver is not taken into account and it may affect the minimum breaking distance in case of severe fog.

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