4 rivers have the same volume of water flow over time but fall from different heights to power hydroelectric dams which dam would provide the most hydroelectric power damaged which is a fall height of 175 ft or dam b which is a fall height of 75 ft
To determine which dam would provide the most hydroelectric power, we need to consider the potential energy of the falling water.
The potential energy of an object is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
Since the rivers have the same volume of water flow over time, we can assume that the mass of water falling per second is the same for all dams. Therefore, we can compare the potential energy by considering only the height.
Dam A, with a fall height of 175 ft:
PE_A = m * g * h_A = m * 9.8 * 175
Dam B, with a fall height of 75 ft:
PE_B = m * g * h_B = m * 9.8 * 75
Comparing the two equations, we can see that Dam A will produce more potential energy, and hence more hydroelectric power, since its fall height is greater:
PE_A > PE_B
Therefore, Dam A, with a fall height of 175 ft, would provide the most hydroelectric power.