The specialty of an athlete on the women's track team is the pole vault. She has a mass of $40$ kg and her approach speed is $8$ m$/$s$.$ When she is directly above the bar, her speed is $1\mathrm{.}7$ m$/$s$.$ Neglecting air resistance and any energy absorbed by the pole, determine the amount$($in m$)$ she has raised herself as she crosses the bar.