$($b$)(4$ points$)$ If instead the water resistance is quadratic in the velocity, so that Newton's

second law gives

$($dv$)/($dt$)=$g$-($b$)/($m$)$v$^(2)$

find the object's velocity as a function of time t$($dv$)/($dt$)=$g$(1-$k$^(2)$v$^(2))$ where k$=\backslash$sqrt$(($b$)/($m$)$g$).$ Then the

algebra is a little less messy. After obtaining the final answer in terms of k$,$ remember to

replace k by $\backslash$sqrt$(($b$)/($m$)$g$).$