tough question (1 Viewer)

[little master]

i was wondering if any 1 culd explain how to do this question

the amount of fuel Fin litres required per hour to propel a plane in level flight at a constant speed is u km/h is given by F=Au^3+ B/u
where A and B are constants

(i) show tht a pilot wishing to remain in level flight for as long as possible shuld fly at [B/3A]^1/4 km/h

ii)show that a pilot wishing to fly as far as possible in level flight should fly approximately 32% faster than the speed given in part (i).

i got part 1 but having trouble with part 2

i kno its late but if any 1 culd hep.. really appreciated
thanks

 

[bambii]

rate of fuel/km= fuel/ speed

=F/u
sub in F= Au^3 +B/u

=Au^2 + B/u^2


find minimum fuel usage so max distance

so dr/du=0

2Au - 2B/u^3

...

u=(B/A)^(1/4)

show its a min through second derivative

then use that over answer in (i) to show how much faster the plane should travel

ie. [(B/A)^(1/4)]/ [(B/3A)^1/4]