To determine which dam would provide the most hydroelectric power, we need to consider the height from which the water falls, as gravitational potential energy is a key factor in generating hydroelectric power.
The formula for the potential energy (which translates into power generation when water falls) is given by:
\[ PE = mgh \]
Where:
- \( PE \) is the potential energy,
- \( m \) is the mass of the water,
- \( g \) is the acceleration due to gravity (which is constant),
- \( h \) is the height of the fall.
Since the volume of water flow is the same for each dam, the mass of the water will be proportional to the volume, and \( g \) is constant for all scenarios. Therefore, the potential energy is directly proportional to the height of the fall.
Now let's look at the heights for each dam:
- Dam A: 175 feet
- Dam B: 75 feet
- Dam C: 135 feet
- Dam D: 100 feet
Since Dam A has the greatest height of 175 feet, it will produce the most hydroelectric power.
The correct answer is: Dam A: fall height of 175 feet.