Problem $2(20$ pts$.)$: A city engineer is tasked with evaluating the signal timing at a key intersection that spans $50$ feet in width, with a posted speed limit on the approach roads of $45mph.$ Provided parameters for this assessment include an average vehicle length of $22$ feet, a deceleration rate as per the city's guidelines of $10(f\frac{t}{s^2}),$ and a perception$-$reaction time of $1\mathrm{.}5$ seconds.

A$.$ Calculate the yellow light duration based on these given parameters.

B$.$ Assess the required adjustments to the yellow light duration if the posted speed is to be increased by $10\%$ or decreased by $10\%.$

$5$ pes

C$.$ Discuss how changes in the posted speed, without corresponding adiustments to light duration, could affect the Dilem $Z,$ withous corresponding adjustments to the yellow

$($Show all your work! Provide units with your answer and circle your answer.$)$