# Total energy of an airplane, work done against air resistance

## Homework Statement

An airliner of mass 300 tonnes is powered by four engines, each developing 15 000 kW. Its speed at take-off is 75 m(s^1), and it takes 11 minutes to reach its cruising speed of 210 m(s^1) at a height of 10 000 metres. Calculate the work done against air resistance during the climb.

## The Attempt at a Solution

Alright so I have reasoned that (total energy at take-off)+(work done by engines)+(W, work done against air resistance)=(total energy at 10 000 metres) and that:
Total energy at take-off = PE +KE = 0 + (0.5 x 300 000 x (75^2))
Work done by engines (in 11 minutes) = (60 000 000)/(660)
Total energy at 10 000 metres = PE + KE = (10 000 x 300 000g) + (0.5 x 300 000 x (210^2))
G=10

Which makes W (work done against air resistance) = ((10 000 x 300 000 x 10) + (0.5 x 300 000 x ((210^2)) – (0.5 x 300 000 x (75^2)) – ((60 000 000)/(660))) = 3.58 x (10^10) J correct to 3 s.f.

However, the correct answer is 3.83 x (10^9) J.
What mistake(s) did I make?

(total energy at take-off)+(work done by engines)+(W, work done against air resistance)=(total energy at 10 000 metres)

I think that the above equation must be

(total energy at take-off)+(work done by engines) = (W, work done against air resistance) + (total energy at 10 000 metres)

Work done by engines (in 11 minutes) = (60 000 000)/(660)

Note that Energy = Power x time

thanks!