Calculating the Kinetic Energy of a Man 20 Meters Above Water

To determine the kinetic energy of the man when he is 20 meters from the water, we need to use the principles of conservation of energy. At the top of the cliff, the man has potential energy which gets converted into kinetic energy as he falls. First, calculate the initial potential energy (PE_initial) at the top of the cliff using the formula: \[ \text{PE} = m \cdot g \cdot h \] Where: - \( m = 100 \) kg (mass of the man) - \( g = 9.8 \) m/s² (acceleration due to gravity) - \( h = 50 \) meters (height of the cliff) \[ \text{PE_initial} = 100 \cdot 9.8 \cdot 50 = 49,000 \text{ J} \] Next, calculate the potential energy (PE_final) when he is 20 meters from the water (30 meters from the top): \[ \text{PE_final} = m \cdot g \cdot h \] Where: - \( h = 50 - 20 = 30 \) meters (he has fallen 30 meters) \[ \text{PE_final} = 100 \cdot 9.8 \cdot 30 = 29,400 \text{ J} \] The difference in potential energy is converted into kinetic energy as he falls: \[ \text{KE} = \text{PE_initial} - \text{PE_final} \] \[ \text{KE} = 49,000 \text{ J} - 29,400 \text{ J} = 19,600 \text{ J} \] So, the kinetic energy of the man when he is 20 meters from the water is: \[ 19,600 \text{ J} \] Therefore, the correct answer is: \[ \boxed{19,600 \text{ J}} \]