Problem $2.[20$ points$]$

A section of major four$-$lane undivided highway has the following flow$-$density relationship:

$q=50k-0\mathrm{.}156k^2$

A minor road intersects this major highway section with a stop sign at the intersection. When traffic flow reaches capacity $($maximum flow$)$ on major highway, what is the minimum sight distance from the intersection along major highway for the passenger car on the minor road to have safe maneuvering after stopping at the intersection? Assume the approach grade on the minor road is $4\%.$

Table $7\mathrm{.}8$ Time Gap for Case B$1-$Left Turn from Stop

$\backslash$table$[[$Design Vehicle,Time Gap $(t_g)($second$)$ at Design Speed of Major Road$],[$Passenger Car,$7\mathrm{.}5],[$Single$-$unit Truck,$9\mathrm{.}5],[$Combination Truck,$11\mathrm{.}5]]$

Nole: Time gaps are for a stopped vehicle to turn left onlo a two$-$lane highway with no median and grade $3$ percent or less. The table values require adjustment as follows: For multilane highways:

For left turns onto two$-$way highways with more than two lanes, add $0\mathrm{.}5$ seconds for passenger cars or $0\mathrm{.}7$ seconds for trucks for each additional lane. from the left, in excess of one, to be crossed by the turning vehicle. For minor road approach grades:

If the approach grade is an upgrade that exceeds $3$ percent, add $0\mathrm{.}2$ seconds for ench percent grade for loft turns