Total energy of an airplane, work done against air resistance

[furor celtica]

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.

Homework Equations

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?

 

[grzz]

(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)

 

[grzz]

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

Note that Energy = Power x time

 

[furor celtica]

thanks!

 

[asteriatic]

It seems like you have made a small calculation error in your equation for the work done against air resistance. The correct equation should be W = (PE at 10,000m + KE at 10,000m) - (PE at take-off + KE at take-off) - (work done by engines). This will give you the correct answer of 3.83 x (10^9) J. Additionally, it is important to note that the work done by the engines should be calculated in joules per second (Watts), so you will need to multiply your result by 11 minutes (660 seconds) to get the correct value. Other than that, your approach and reasoning seem to be correct.