To find the height the hiker climbed, we can use the formula for gravitational potential energy:
\[ PE = mgh \]
where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height (in meters).
Rearranging the formula to solve for height \( h \),
\[ h = \frac{PE}{mg} \]
Given:
- \( PE = 470,000 , \text{J} \)
- \( m = 80 , \text{kg} \)
- \( g = 9.81 , \text{m/s}^2 \)
Substituting the values into the equation:
\[ h = \frac{470,000 , \text{J}}{80 , \text{kg} \times 9.81 , \text{m/s}^2} \]
Calculating the denominator:
\[ 80 , \text{kg} \times 9.81 , \text{m/s}^2 = 784.8 , \text{kg m/s}^2 \]
Now substituting back:
\[ h = \frac{470,000 , \text{J}}{784.8 , \text{kg m/s}^2} \approx 599.19 , \text{m} \]
Rounding to the nearest hundred:
\[ h \approx 600 , \text{m} \]
So, the height the hiker climbed is approximately 600 meters.
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