What is the gravitational potential energy of an 85 kg mountain climber at the summit of a 6267 m volcano?P.E = mgh

1. ### Break Down the Problem

To calculate the gravitational potential energy (P.E) of the mountain climber, we will:

1. Identify the mass (m) of the climber.
2. Identify the height (h) of the volcano.
3. Identify the acceleration due to gravity (g).

2. ### Relevant Concepts

The formula for gravitational potential energy is given by: $P.E = mgh$ Where:

• $m$ = mass of the object (kg)
• $g$ = acceleration due to gravity $(9.81 \, \text{m/s}^2)$
• $h$ = height above the reference point (m)

3. ### Analysis and Detail

We have:

• $m = 85 \, \text{kg}$
• $h = 6267 \, \text{m}$
• $g = 9.81 \, \text{m/s}^2$

Now we will substitute the values into the formula: $P.E = 85 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 6267 \, \text{m}$

4. ### Verify and Summarize

Calculating the potential energy:

1. Calculate $85 \, \text{kg} \times 9.81 \, \text{m/s}^2$: $= 835.85 \, \text{N}$
2. Now multiply by the height: $P.E = 835.85 \, \text{N} \times 6267 \, \text{m} = 523,224,969.95 \, \text{J}$

Final Answer

The gravitational potential energy of the mountain climber at the summit of the volcano is approximately $523,225 \, \text{J}$ (Joules).