[填空题]
A water tank in the t1y mo6 osoi25smzh3k(+eud- *cmmece 1l5 ed2 hape of a rectangular prism has height 4$ \mathrm{~m}$ and a base of 3 $\mathrm{~m} \times 2 \mathrm{~m}$ . Water flows out of a tap at the bottom of the tank at a rate proportional to the square root of the depth of the water at any given time. Let h denote the depth of the water, in metres, and V is the volume of the water remaining in the tank after t minutes.
1. Write down a differential equation for the rate of change of volume of water in terms of time.
2. Show that the volume of water in the tank is given by V=6 $\mathrm{~h} \mathrm{~m}^{3}$ at time t .
V= h.
3. Hence, or otherwise, show that a differential equation for the rate of change of water height in terms of time is
4. Given that the tank is initially full, and the height then drops 3 $\mathrm{~m} $ after 48 minutes, solve the differential equation in part (c).
h=$\left(a-\frac{t}{b}\right)^{2}$;a= ,b= .
5. Find the time it takes for the tank to empty.
t= minutes.
