Ball's Mechanical Energy at 3m from Ground: Kinetic + Potential Energy

To determine the mechanical energy of the ball, you need to consider both its kinetic energy and its potential energy. 1. **Kinetic Energy (KE):** The kinetic energy of the ball can be calculated using the formula: \[ KE = \frac{1}{2}mv^2 \] where \( m \) is the mass of the ball and \( v \) is its velocity. Given: - \( m = 0.1 \, \text{kg} \) - \( v = 12 \, \text{m/s} \) \[ KE = \frac{1}{2} \times 0.1 \times 12^2 \] \[ KE = 0.05 \times 144 \] \[ KE = 7.2 \, \text{J} \] 2. **Potential Energy (PE):** The potential energy of the ball can be calculated using the formula: \[ PE = mgh \] where \( m \) is the mass of the ball, \( g \) is the gravitational acceleration (approximately \( 9.8 \, \text{m/s}^2 \)), and \( h \) is its height above the ground. Given: - \( m = 0.1 \, \text{kg} \) - \( g = 9.8 \, \text{m/s}^2 \) - \( h = 3 \, \text{m} \) \[ PE = 0.1 \times 9.8 \times 3 \] \[ PE = 0.1 \times 29.4 \] \[ PE = 2.94 \, \text{J} \] 3. **Total Mechanical Energy (TME):** The total mechanical energy of the ball is the sum of its kinetic and potential energies: \[ TME = KE + PE \] \[ TME = 7.2 + 2.94 \] \[ TME = 10.14 \, \text{J} \] So, the correct answer is: \[ \boxed{10.14 \, \text{J}} \]