A crest curve connects a $+1\%$ initial grade with a $-2\%$ final grade and is designed for $60$ mph$.$

a$.(1$ point$)$ Find the stopping sight distance $($assuming the worst case grade and standard AASHTO values for reaction time and deceleration rate$).$ Express your answer in feet and round to the nearest whole number.

b$.(2$ points$)$ What is the minimum length of the curve to ensure adequate sight distance for a driver with an eye height of $3$ feet to see a $2$ feet tall object? Express your answer in feet and round to the nearest whole number.

c$.(1$ point$)$ Now assume you are designing the same curve with a $+1\%$ initial grade, a $-2\%$ final grade, and $60$ mph$,$ but this time, determine the length using the appropriate K$-$value.

d$.(1$ point$)$ Briefly discuss the differences between your answers to parts b and c$.$