(Solved): 3. (III) A scale is adjusted so that when a large, shallow pan is placed on it, it reads zero. A wa ...

3. (III) A scale is adjusted so that when a large, shallow pan is placed on it, it reads zero. A water faucet at height $h=2.5\mathrm{m}$ above is turned on and water falls into the pan at a rate $R=0.14\mathrm{kg}/\mathrm{s}$. Determine $(a)$ a formula for the scale reading as a function of time $t$ and $(b)$ the reading for $t=9.0\mathrm{s}$. (c) Repeat $(a)$ and (b), but replace the shallow pan with a tall, narrow cylindrical container of area $A=20{\mathrm{cm}}^2$ (the level rises in this case).