Calculate Potential Energy Lost for Man Falling 20m from Water

To determine the kinetic energy of the diver when he is 20 meters above the water, we need to consider the principles of energy conservation, specifically potential and kinetic energy. Initially, when the diver is at the top of the 50-meter cliff, all his energy is gravitational potential energy (assuming no initial kinetic energy). The potential energy (PE) at the top is given by: \[ PE = mgh \] where: \( m \) = mass (100 kg) \( g \) = gravitational acceleration (approximately 9.8 m/s²) \( h \) = height (50 meters) \[ PE_{\text{initial}} = 100 \times 9.8 \times 50 = 49,000 \, \text{J} \] As the diver falls and reaches 20 meters above the water, his potential energy decreases and is converted into kinetic energy (KE). The potential energy at 20 meters is: \[ PE_{\text{final}} = mgh = 100 \times 9.8 \times 20 = 19,600 \, \text{J} \] The loss in potential energy is converted into kinetic energy. The initial potential energy minus the final potential energy gives us the kinetic energy at 20 meters: \[ KE = PE_{\text{initial}} - PE_{\text{final}} \] \[ KE = 49,000 \, \text{J} - 19,600 \, \text{J} = 29,400 \, \text{J} \] Therefore, the correct answer is: \[ \boxed{29,400 \, \text{J}} \]