Problem statement:

A new power plant is planned to be built in a rural region and is expected to emit $P{M}_{2\mathrm{.}5}$ at a rate of $0\mathrm{.}09k\frac{g}{s}$ from a $100m$ stack. For simplicity, assume a plume rise of $50m$ and that the prevailing wind is westerly $($blows from west to east$)$ at a speed of $1\mathrm{.}8\frac{m}{s}.$

You are tasked with developing a model to predict $P{M}_{2\mathrm{.}5}$ surface concentrations from the stack emissions. Consider two scenarios: $($i$)$ a fall cloudy night and $($ii$)$ a fall afternoon. For the purposes of this homework, assume that these two scenarios are representative of night$-$time and day$-$time surface concentrations, respectively.

Produce a figure of day$-$time and night$-$time surface $P{M}_{2\mathrm{.}5}$ concentrations in $\frac{g}{m^3}($both on the same plot$)$ for distances ranging between $0\mathrm{.}1km$ and $100km$ east of the stack. Hint: For better visualization, show the distances in log$-$scale. Briefly discuss the implications of the power$-$plant pollution emissions for communities located $10km-20km$ east of the power plant $($just $2-3$ sentences$).(50$ pts$)$

The company that owns the power plant plans to build pickleball courts $($fastest growing sport in the U$.$S$.!)$ for the staff who wish to do some physical activity during breaks. Due to road access limitations$,$ the courts can be located at either $3km$ or $5km$ east of the stack, with room to move $1km$ north or south at each of the locations. The $P{M}_{2\mathrm{.}5}$ concentrations at the courts are to be maintained below $10\frac{g}{m^3}$ at all times. Could this be achieved at any of the locations? Briefly discuss the results $($just $2-3$ sentences$).(50$ pts$)$