Question $5$

There are mainly two friction components for a vehicle running on a flat road: the resista

wheels $(F_r)$ and the drag force due the air flows around the car$(F).$ The two ficsistance from the

defined as$,F_r=f*W$

$F_d=\frac{1}{2}*C_d*A**U^2,$ where $f$ and $C_d$ are some constants, $Wis$ the weight $of$ the car, $Ais$

the projected frontal area, $U$ is the velocity of the car and $$ is the local air density, which is $1\mathrm{.}1k\frac{g}{m^3}.$

Assume the frontal area of the car be $10m^2$ with a total mass of $30000$ kg $.$ The constants $f$ and $C_d$ are

measured to be $0\mathrm{.}65$ and $0\mathrm{.}0069,$ respectively. Assume the car has an engine with $85\%$ efficiency, the

fuel density is $900k\frac{g}{m^3}$ and it has an energy content of $44M\frac{J}{k}g.$ The car is moving at a speed of

$27\mathrm{.}78\frac{m}{s}.$

a$)$ Determine the power needed to be supplied to the car to overcome the total frictional forces.

$(5$ points$)$

b$)$ Find the total amount of work input needed to drive the car for a five hours trip from Toronto to

Montreal.

$(5$ points$)$

c$)$ Evaluate the distance the car can be driven for $1$ L of the fuel.

$(10$ points$)$