What is the efficiency of the engines?

[Lyphta]

Homework Statement

A 3250 km aircraft takes 12.5 minutes to achieve its cruising altitude of 10 km and cruising speed of 850 km/h. If the plane's engines deliver, on the average, 1500 hp of power during this time, what is the efficiency of the engines?

Homework Equations

Efficiency = Power output / Power input x 100
P = W/t --> P= mgh/t, P=Fdcos(theta)/t

The Attempt at a Solution

m = 3250 kg
t = 12.5 min --> 750 sec
h = 10 km --> 10000 m
Pin = 1500 hp --> 1119000 Watts
v = 850 km/h --> 236.11 m/s

vf = at +vi (attempt to find the velocity components but don't add up right)
236.11 = a (750) + 0
a = .315 m/s^2

average v = vf/2
= 236.11/2
average v = 118 m/s

Poutx = F(average v) = ma(average v)
= 3250(.315)(118)
= 120802.5 W

Piny = Fd/t = mgh/t
= 3250(9.81)(10000)/750
= 425100 W

The real answer is 4.091 x 10^8 J ; e = 48.7% but I don't know how to get that answer...

 

[rl.bhat]

Acceleration can be found by v^2 = u^2 + 2as. This acceleration is in addition to the acceleration due to gravity. So the actual acceleration of the aircraft is a+g. Now find the work done.

 

[Lyphta]

by u, do you mean initial velocity? or potential energy?

 

[rl.bhat]

It is initial velocity, which is zero in this case.