To determine which dam would provide the most hydroelectric power, we need to consider the height from which the water falls, as the potential energy available for conversion to electricity is directly related to the height of the fall.
The higher the fall, the more potential energy the water has. This potential energy can be calculated with the formula:
\[ \text{Potential Energy} = mgh \]
where:
- \(m\) = mass of the water
- \(g\) = acceleration due to gravity (constant, approximately 9.81 m/s²)
- \(h\) = height of the fall (in meters)
Since all four rivers have the same volume of water flow and therefore the same mass of water, the only factor that will determine the power generated by each dam is the height of the fall.
Looking at the heights given:
- Dam A: 175 feet
- Dam B: 75 feet
- Dam C: 135 feet
- Dam D: 100 feet
Among these, Dam A has the highest fall at 175 feet. Therefore, it would provide the most hydroelectric power.
So the answer is: Dam A: fall height of 175 feet.