vertical curve connects a $+1\mathrm{.}0\%$ initial grade with a $-3\mathrm{.}0\%$ final grade and is designed for $50$

mph$.$ The station of the PVI is $250+00$ with an elevation of $1,200$ ft$.$ 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? To answer this question, first find the stopping sight distance $($assuming

the worst case grade and standard AASHTO values for reaction time and deceleration rate$),$

and then determine the length of the curve. Express your answer in feet.