To determine which dam would provide the most hydroelectric power, we need to consider the height from which the water falls (the potential energy) and the volume of water flow (the flow rate).
The potential energy (and thus the power generated) is proportional to both the height of the fall and the volume of water. The formula for gravitational potential energy is:
\[ \text{Potential Energy} = m \times g \times h \]
where:
- \( m \) is the mass of the water (related to volume and density),
- \( g \) is the acceleration due to gravity,
- \( h \) is the height of the fall.
Since all the rivers have the same volume of water flow, the key factor that will influence the amount of hydroelectric power generated is the height of the fall.
Given 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 of 175 feet, which means it would generate the most hydroelectric power. Therefore, the answer is:
Dam A: fall height of 175 feet.