$($a$)$ Calculate the height $($in m$)$ of a cliff if it takes $2\mathrm{.}13$ s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of $8\mathrm{.}19$ m$/$s$.($Enter a number.$)\_\_\_\_\_\_\_\_\_$m

$($b$)$How long $($in s$)$ would it take to reach the ground if it is thrown straight down with the same speed? $($Enter a number.$)\_\_\_\_\_\_\_\_\_\_\_$s