I drop a \( 60-\mathrm{g} \) golf ball from 2.0 m high. It rebounds to 1.5 m . How much energy is lost? 1) 0.29 J 2) 0.50 J 3) 0.88 J 4) 1.0 J 5) 1.1 J

To find the energy lost during the rebound of the golf ball, we can calculate the potential energy at the initial height and the potential energy at the rebound height, then find the difference. The potential energy (PE) is given by the formula: \[ PE = mgh \] where \( m \) is the mass, \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \mathrm{m/s^2} \)), and \( h \) is the height. 1. **Initial Potential Energy (2.0 m):** \[ PE_{\text{initial}} = 0.06 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 2.0 \, \text{m} = 1.176 \, \text{J} \] 2. **Rebound Potential Energy (1.5 m):** \[ PE_{\text{rebound}} = 0.06 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 1.5 \, \text{m} = 0.882 \, \text{J} \] 3. **Energy Lost:** \[ \text{Energy lost} = PE_{\text{initial}} - PE_{\text{rebound}} = 1.176 \, \text{J} - 0.882 \, \text{J} = 0.294 \, \text{J} \] So the energy lost when the golf ball rebounds is approximately \( 0.29 \, \text{J} \). The correct answer is **1) 0.29 J**.