The gravitational potential energy (PE) can be calculated using the formula:
\[ PE = m \cdot g \cdot h \]
where:
- \( m \) 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 above the reference point (in this case, the pool's surface).
Plugging in the values:
- \( m = 68 , \text{kg} \)
- \( g = 9.81 , \text{m/s}^2 \)
- \( h = 7.5 , \text{m} \)
Now, substituting these values into the formula:
\[ PE = 68 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 7.5 , \text{m} \]
Calculating it step-by-step:
- \( 68 \cdot 9.81 = 667.08 , \text{N} \)
- \( 667.08 \cdot 7.5 = 5003.1 , \text{J} \)
Thus, the gravitational potential energy is approximately \( 5003.1 , \text{J} \).
Rounding this to closely match the given options, the answer is:
4998 J (This is the correct option that is closest to our calculated value.)