Question

The air surrounding an airplane in flight exerts a drag force that acts opposite to the airplane's motion. When an Airbus A380 is flying in a straight line at a constant altitude at a constant 250 m/s, each of the four jet engines on the Airbus A380 develops a thrust force of 322,00N. What is the rate at which the drag force does work on the Airbus A380? Note: one horse power (hp) is 764W.

Answer 1

`4.32\cdot 10^5 hp`,
`3.22\cdot 10^8 W`

Step-by-step explanation:

The jet is flying at constant velocity: this means that its acceleration is zero, so the net force acting on the jet is also zero.

Therefore, we can write:

`4F_T - F_d = 0`

where

`F_T = 322,000 N` is the thrust force generated by each engine of the jet

`F_d` is the drag force

Solving for Fd,

`F_d = 4 F_T = 4(322,000)=1.288\cdot 10^6 N`

The velocity of the jet is

`v=250 m/s`

So, the rate at which the drag force does work (which is the power) is

`P=F_d v`

and substituting

`F_d = 1.288\cdot 10^6 N\\v = 250 m/s`

we find

`P=(1.288\cdot 10^6)(250)=3.22\cdot 10^8 W`

Converting into horsepower,

`P=(3.22\cdot 10^8)/(746)=4.32\cdot 10^5 hp`