To determine which dam would provide the most hydroelectric power, we need to consider the height from which the water falls, as well as the volume of water flow (which is the same for all in this case). The potential energy of the water, which is converted to electricity in hydroelectric dams, is directly related to the height of the fall.
The formula for gravitational potential energy (PE) is: \[ PE = mgh \] where:
- \( m \) is the mass of the water (which can be related to flow rate),
- \( g \) is the acceleration due to gravity (approximately \(9.81 m/s^2\)),
- \( h \) is the height of the fall.
Since the mass and gravitational constant are the same for all dams, the height of the fall (h) is the determining factor.
Here are the fall heights for each dam:
- Dam A: 175 feet
- Dam B: 75 feet
- Dam C: 135 feet
- Dam D: 100 feet
Based on the heights:
- Dam A, with the highest fall at 175 feet, would provide the most hydroelectric power.
Therefore, the answer is: dam A: fall height of 175 feet.