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## Homework Statement

Calculate the gain of potential energy of a mountaineer of mass 80kg who travels to the top of the mountain Everest 9km above sea level.

## Homework Equations

ΔEp=mgΔh

## The Attempt at a Solution

ΔEp=mgΔh=80x9.81x9x10^3=7.1x10^6J.

This is the correct answer but surely it's only an estimate since the value of g 9km above the Earth's surface is 9.83830. Δg=9.8380-9.81= 2.8x10^(-3)?

Is it possible to calculate the exact change is Ep as the mass moves through Δh, rather than using a fixed value of 9.81?