$6\mathrm{.}87.*$A $120-$lbm parachutist jumps from a plane and falls in free fall for a while before opening her chute.

$($a$)$ If she falls head first, then her projected area perpendicular to the direction of fall is $\backslash (\backslash$approx $1\backslash$mathrm$\{$ft$\}^\{2\}\backslash )$ and $\backslash ($ C$\_\{$d$\}\backslash$approx $0\mathrm{.}7\backslash ).$ What is her terminal velocity? How many seconds must she fall to reach $99$ percent of this terminal velocity, assuming that the drag coefficient is independent of velocity? How far does she fall in this number of seconds?

$($b$)$ If instead of falling head first, she spreads out her arms and legs and lies horizontally, then her projected area will be $\backslash (\backslash$approx $6\backslash$mathrm$\{$ft$\}^\{2\}\backslash )$ and $\backslash ($ C$\_\{$d$\}\backslash$approx $1\mathrm{.}5\backslash ).$ Repeat part $($a$)$ for this condition.