High$-$speed elevators function under two limitations: $(1)$ the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about $1\mathrm{.}2$ m$/$s$2$

$,$ and $(2)$ the typical maximum speed attainable is about $8\mathrm{.}9$ m$/$s

$.$ You board an elevator on a skyscraper's ground floor and are transported $220$ m

above the ground level in three steps: acceleration of magnitude $1\mathrm{.}2$ m$/$s$2$

from rest to $8\mathrm{.}9$ m$/$s

$,$ followed by constant upward velocity of $8\mathrm{.}9$ m$/$s

$,$ then deceleration of magnitude $1\mathrm{.}2$ m$/$s$2$

from $8\mathrm{.}9$ m$/$s

to rest. Part $1$: Determine the elapsed time for each of these $3$ stages. Part $2$: Determine the change in the magnitude of the normal force, expressed as a $\%$

of your normal weight during each stage.