Question

An 75-kg hiker climbs to the summit of Mount Mitchell in western North Carolina. During one 2.0-h period, the climber's vertical elevation increases 540 m. Determine the change in gravitational potential energy of the climber-Earth system.

Answer 1

The change in gravitational potential energy of the climber-Earth system is
`\Delta PE = 396900 \ J`

Step-by-step explanation:

From the question we are told that

The mass of the hiker is
`m = 75 \ kg`

The time taken is
`T = 2 \ hr = 2 * 3600 = 7200 \ s`

The vertical elevation after time T is
`H = 540 \ m`

The change in gravitational potential is mathematically represented as

`\Delta PE = mgH`

here g is the acceleration due to gravity with value
`g = 9.8 \ m/s^2`

substituting values

`\Delta PE = 75 * 9.8 * 540`

`\Delta PE = 396900 \ J`