Problem $3$

At a signalized intersection approach $($northbound$),$ the speed limit is $45$ mph $.$ The width of the cross street $($east approach$)$ is $72$ ft $.$ If the length of the design vehicle is $16$ ft $,$ what should be the yellow and all$-$red times $($to the next $0\mathrm{.}5$ sec $).$ Use perception$/$reaction time of $1\mathrm{.}0$ sec $,$ and deceleration rate of $10\mathrm{.}0f\frac{t}{s^2}.$ Assume $0\%$ grade.