Problem #$5$

The grade into a vertical sag curve is $-2\%.$ The curve length is $1,400ft.$ The grade out of the curve is $+4\%.$ The elevation and station of the grade intersection are $226\mathrm{.}88ft$ and $7+20\mathrm{.}00,$ respectively. The curve goes through a flood plain where the $50-$year flood elevation is $240ft.$

$($a$)$ Find the stations where the curve drops below and emerges from the $50-$year flood plain.

$($b$)$ What length of curve will be submerged in a $50-$year flood?

$($c$)$ How will increasing the length of curve change the length of the curve that will be submerged?

$($d$)$ How will decreasing the length of the curve change the length of the curve that will be submerged?

$($e$)$ What can be done to the pavement so that flooding will not degrade it$?$