Water flows over a section of Niagara Falls at a rate of \( 1.20^{\prime} 10^{6} \mathrm{~kg} / \mathrm{s} \) and falls 50.0 m . What is the power dissipated by the waterfall? 1) 588 MW 2) 294 MW 3) 147 MW 4) 60.0 MW 5) 25.0 MW

To find the power dissipated by the waterfall, we can use the formula for gravitational potential energy and power: \[ P = \frac{E}{t} = \frac{mgh}{t} = mg \cdot h \cdot \frac{1}{t} \] Since the mass flow rate is given as \(1.20 \times 10^6 \, \mathrm{kg/s}\), we can write \( m/t = 1.20 \times 10^6 \, \mathrm{kg/s} \). The height \( h \) the water falls is 50.0 m, and \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \mathrm{m/s^2} \). Now, plugging in the values: \[ P = 1.20 \times 10^6 \, \mathrm{kg/s} \cdot 9.81 \, \mathrm{m/s^2} \cdot 50.0 \, \mathrm{m} \] \[ P = 1.20 \times 10^6 \cdot 9.81 \cdot 50.0 \] \[ P = 588.6 \times 10^6 \, \mathrm{W} = 588 \, \mathrm{MW} \] Thus, the correct answer is **1) 588 MW**. Power dissipated by the waterfall can creatively be seen as the "electric output" it could potentially generate if harnessed, illustrating nature's ability to create significant energy through motion. Many famous waterfalls, including Niagara Falls, are not only majestic but also serve as sources of renewable energy. Hydroelectric power plants utilize the energy from falling water to generate electricity, showcasing a brilliant way to harness natural resources for modern needs without carbon emissions!