A farmer is monitoring the growth of a crop over a $120$-day period. The height of the crop in centimeters is given by the function $h(t)=\begin{cases}\frac95t^2,\text{ if }0\le t<60\\ -\frac95\left(t^2-240t+120\right),\text{if }60\le t<120\end{cases}$ , where $t$ is the time in days since initially planting their crops. When is the growth rate of the crop at a maximum?