$3.$ Use phase impacts: Vehicles are powered by fuel of various types. We would usually think about the gasoline and the electricity used to power all the mowers, but we should also think about the calories expended during the mowing for the push mowers. For the push mowers, the environmental impacts associated with $$fueling$$ will depend on both the cost of the fuel $($gas or electricity$)$ and the calories burned, and therefore how hilly the terrain is$.$

a$)$ In one sentence, define a kilowatt$-$hour $($kWh$).$

b$)$ Assume the battery for the push mower is charged for $4\mathrm{.}5$ hours once a week and consumes energy at a rate of $1$ kW when charging. Assume that you will need to mow from the beginning of May through the end of October $(24$ weeks$).$ If electricity generation in Michigan emits $0\mathrm{.}18$ kg CO$2$ per kWh electricity generated, calculate the total carbon emissions $($kg CO$2$ per year$)$ associated with charging during one year of mowing.

c$)$ Assume the gas mower has an average fuel economy of $0\mathrm{.}5$ gallons per hour and assume the combustion of the fuel produces $9$ kg of CO$2$ per gallon of fuel. If you take $2$ hours to mow the acre and you need to do this once a week over the same mowing months as part b$,$ calculate the total carbon emissions $($kg CO$2$ per year$)$ associated with the gas powered mower.

d$)$ Suppose the average adult burns $200$ Calories per hour $($kcal$/$hr$)$ of mowing a flat acre and $450$ kcal$/$hr on a hilly acre of grass with a push gas mower. Assume the electric mower is $60\%$ of the weight and that this cuts the calories burned for both types of grass field in half. Assume the average person consumes $2,000$ kcal per day. Providing $2,000$ kcal of energy generates approximately $4\mathrm{.}5$ kg CO$2$ equivalent for an average diet. Calculate the emissions $($kg CO$2/$yr$)$ associated with extra food consumption to fuel one year of mowing on Saturdays $($using the months where mowing is required as given in part b and an estimate of $2$ hours to mow the acre of land$)$ with both types of push mower, on both hilly and flat terrain.

e$)$ Assume that the autonomous mower is programmed to mow in a random walk $($like a Roomba$).$ This increases the time required to mow the acre of grass from $2$ hours to $21$ hours $($this time includes the time needed to recharge for $1$ hour every $90$ minutes$).$ Assume that the autonomous mower requires no oversight and that it leaves the trimmed grass blades on the lawn. The lawn needs to be mowed like this twice a week $($for the same number of weeks as the other mowers$)$ and the charging ends up being $9$ hours out of every $21$ hour mowing period. What are the annual CO$2$ emissions associated with the autonomous mower assuming the charging energy consumption and CO$2$ emissions are the same as was given in part b$.$

f$)$ Compare the use$-$phase emissions for mowing a flat acre with the electric push mower $($including charging the batteries and eating extra food$)$ with those associated with the gas powered push mower $($eating extra food$)$ and the autonomous mower $($charging batteries only$).$ Assume flat terrain. Calculate the annual emission savings $($kg CO$2$ per year$)$ associated with:

$1)$ Using the electric mower vs$.$ the gas powered. Does it reduce use$-$phase carbon emissions?

$2)$ Switching from the push battery powered to the autonomous mower. Does it reduce use$-$phase carbon emissions?

g$)$ The electric mower is clearly better from a carbon emissions standpoint compared to the autonomous mower, but there are hidden costs associated with it$.$ The upfront cost of the electric push mower is $$200$ and the cost of the autonomous mower is $$2000.$ How much would you need to spend for each method for $5$ years $($purchase once and then use for $5$ years$)?$ Assume that the person pushing the electric mower is being paid $$30/$hr and you are purchasing carbon offsets where the offset covers carbon emissions of $1$ metric ton $(1000$ kg$)$ at a cost of $$20.$ Also assume there are no increases in any costs associated with this calculation.

h$)$ Calculate the payback period $($in years$)$ associated with replacing the gas powered mower with the electric push mower.