Question $1$

a$)$ Estimate how much more fuel a Boeing $747-300$ has to carry on a flight from Vancouver International Airport to London Heathrow Airport to accommodate for laptop use in flight. Assume that everyone on the plane has a laptop and that the jet fuel is converted to electricity with an efficiency of $0\mathrm{.}33.$

b$)$ How does the cost of transport of a Boeing $747-300$ compare to that of a $2010$ Toyota Prius, which has a fuel economy of $4\mathrm{.}7$ L$/100$ km$?$ Compare is terms of L$/100$ km$/$passenger$.$ Assuming the average number of passengers in Toyota to be $1\mathrm{.}5.$

c$)$ How much fuel does a plane require to go from rest on the runway to the cruising speed at their typical altitude?

Hint: Consider the potential energy and kinetic energy required to get the plane to altitude and to speed. Assume that the plane gets to cruising speed almost immediately and spends $20$ mins gaining altitude. Assume that it takes $20$ min for the plane to reach cruising altitude. Remember to account for drag. Note that the drag force acts on the airplane wings, not on its cross$-$sectional area. Include engine$$s efficiency.

d$)$ How much fuel does it cost the plane to fly for $20$ minutes at cruising altitude and cruising speed? Assume air density at cruising altitude to be $0\mathrm{.}4$ kg$/$m$3.$ Compare your answer to part c$).$ Should planes fly at higher or lower altitudes?