We wish to evaluate the difference in power required to operate a vehicle that has an open sun roof compared to the same vehicle that keeps it closed. It has been estimated that with the sun roof open the drag coefficient would be Co $=0\mathrm{.}41,$ while if it remains closed it would be C$=0\mathrm{.}32.$ The vehicle projects an area of $1\mathrm{.}7$ m$^2.$ The density of the air is given by

p $=1\mathrm{.}1$ kg$/$m$^3.$ The vehicle runs, in average, $100$ km$/$hr$.$

a$)$ Determine the additional power $($in kW$)$ required to drive the vehicle with the"sun roof" open.

b$)$ If the vehicle travels on average about $32,000$ km$/$year and the gasoline has an energy value of $45,000$ kJ$/$kg$,$ with density p $=0\mathrm{.}75$ kg$/$L$,$ determine the additional annual amount of gasoline $($in L$)$ that would be spent driving with the "sun roof" open.