Problem $2(5$ pts $)$: Diesel engines emit very fine soot particles. In the atmosphere, these soot particles agglomerates with other particles as they "age". Assume the agglomerated soot particles are spherical and initially suspended at a height of $2\mathrm{.}2$ m ; they have a diameter of $0\mathrm{.}5m$ and a density of $1\mathrm{.}1\frac{g}{c}{m}^3.$ Air density is $1\mathrm{.}2k\frac{g}{m^3}$ and viscosity is $1\mathrm{.}72{10}^{-4}gc{m}^{-1}{s}^{-1}.$ How many hours will the soot particles remain suspended before settling to the ground?