+118658 h(t) = 2,5(1-0,035t¨)^0,4 m
when is 9 cm/sec
\(h = 2.5(1-0.035t)^{0.4}\;metres\\ h = 250(1-0.035t)^{0.4}\;cm\\ \frac{dh}{dt} = 250*0.4(1-0.035t)^{-0.6}*(-0.035)\\ \frac{dh}{dt} = -250*0.4*0.035(1-0.035t)^{-0.6}\\ \frac{dh}{dt} = -3.5(1-0.035t)^{-0.6}\\ \mbox{Find time when velocity =9cm/sec}\\ 9=-3.5(1-0.035t)^{-0.6}\\ \left(\frac{-90}{35}\right)^{-1/0.6}=((1-0.035t)^{-0.6})^{-1/0.6}\\ \left(\frac{-18}{7}\right)^{-5/3}=1-0.035t\\ 1-0.035t=\left(\frac{-18}{7}\right)^{-5/3}\\ 1-0.035t=-\left(\frac{7}{18}\right)^{5/3}\\ 0.035t=1+\left(\frac{7}{18}\right)^{5/3}\\ t=\frac{1+\left(\frac{7}{18}\right)^{5/3}}{0.035}\\ \)
(1+(7/18)^(5/3))/0.035 = 34.4912396506397926
So if I haven't made a mistake, the speed will be 9cm/sec after 34.5 seconds
