Question

An 80,000-kg airliner is flying at 900 km/h at a height of 10.0 km. What is its total energy if the total was 0 when the airliner was at rest on the ground?

Answer 1

`1.034xx10^10 J` of which `2.5xx10^9J` is kinetic energy and `7.84xx10^9J` is potential energy.

Explanation:

First, let's get everything into consistent SI base units.

The altitude is 10 000 m and the speed is

`900(km)/h-:3600s/hxx1000m/km=250 m/s`

Okay. Now, we calculate the kinetic energy and the potential energy changes and add them:

`KE=1/2mv^2 = 1/2(80 000)(250)^2=2.5xx10^9J`

`PE=mgh=(80 000)(9.8)(10 000)=7.84xx10^9J`

So, the total energy is `1.034xx10^10 J`

As you can see, roughly 3/4 of that is potential energy. So, the cost in fuel is mostly for the task of lifting the plane to altitude rather than creating speed!