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$30.$ Stopping sight distance $($SSD$)$ is an important part of transportation engineering. SSD is used to determine speed limits on many roads. SSD can be calculated as

$SSD=\frac{V^2}{2g(\frac{a}{g}+-G)}+V{t}_r$

where

$V=$ initial vehicle speed in $f\frac{t}{s}$

$g=$ gravity in $f\frac{t}{s^2}$

$a=$ deceleration rate in $f\frac{t}{s^2}($assume $11\mathrm{.}2f\frac{t}{s^2}$ for this value$)$

$G=$ roadway grade $(+$ or uphill and $-$ for downhill$)$ as a decimal $(2\%$ is $0\mathrm{.}02$ in this equation$)$

$t_r=$ perception or reaction time in seconds $($assume $2\mathrm{.}5$ seconds here$)$

Given the table of parameters below, calculate the posted speed limit sign required for each of the parameter sets in Excel. Do not use "magic numbers" and instead use fixed references where$/$if needed.

$\backslash$table$[[$SSD $($ft$),$G $(\%)],[160,-3\mathrm{.}4],[225,4\mathrm{.}0],[450,-4\mathrm{.}5],[550,5\mathrm{.}6],[700,3\mathrm{.}0],[800,-1\mathrm{.}7]]$