To determine which dam would provide the most hydroelectric power, we need to consider the height from which the water falls. The potential energy of the water, which is converted into electrical energy by the dam, is directly related to the height of the fall. The formula for gravitational potential energy is:
\[ PE = mgh \]
where:
- \( PE \) is the potential energy,
- \( m \) is the mass of the water,
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s²), and
- \( h \) is the height of the fall.
Since all dams have the same volume of water flowing over time, the dam with the highest fall height will produce the most hydroelectric power.
Comparing the heights:
- Dam A: 175 feet
- Dam C: 135 feet
- Dam D: 100 feet
- Dam B: 75 feet
Dam A has the highest fall height at 175 feet. Therefore, dam A would provide the most hydroelectric power.
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