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$5.$

Starting from rest, a $67\mathrm{.}0$ kg woman jumps down to the floor from a height of $0\mathrm{.}710$ m $,$ and immediately jumps back up into the air. While she is in contact with the ground during the time interval $F=9,200t-11,500t^{2}FtN*sN*s\frac{m}{s}\frac{m}{s}\frac{m}{s}\frac{m}{s}0,$ the force she exerts $on$ the floor can $be$ modeled using the function

$F=9,200t-11,500t^2$

where $Fisin$ newtons and $tisin$ seconds.

$(a)$ What impulse $(inN*s)$ did the woman receive from the floor? $(Enter$ the magnitude. Round your answer $toat$ least three significant figures.$)$

$$

$N*s$

$(b)$ With what speed $(in\frac{m}{s})$ did she reach the floor? $(Round$ your answer $toat$ least three significant figures.$)$

$$

$\frac{m}{s}$

$(c)$ With what speed $(in\frac{m}{s})$ did she leave $it?(Round$ your answer $toat$ least three significant figures.$)$

$$

$\frac{m}{s}$

$(d)To$ what height $(inm)$ did she jump upon leaving the floor?

$$

$m$