To solve the problem, we need to analyze the situation step by step, focusing on the concepts of potential energy (PE) and kinetic energy (KE) in the context of gravitational motion. ### Step 1: Understanding Potential Energy The potential energy (PE) of an object at a height \( h \) is given by the formula: \[ PE = mgh \] where: - \( m \) is the mass of the object (in kg), - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)), - \( h \) is the height above the ground (in meters). For our stone: - Mass \( m = 1 \, \text{kg} \) - Height \( h = 10 \, \text{m} \) Calculating the initial potential energy when the stone is at 10 m: \[ PE_{\text{initial}} = 1 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 10 \, \text{m} = 98.1 \, \text{J} \] ### Step 2: Understanding Kinetic Energy The kinetic energy (KE) of an object in motion is given by the formula: \[ KE = \frac{1}{2} mv^2 \] where \( v \) is the velocity of the object. ### Step 3: Finding the Kinetic Energy at 5 m Above the Ground When the stone is at a height of 5 m, it has fallen 5 m from its original height of 10 m. At this point, we can calculate the potential energy at 5 m: \[ PE_{\text{5m}} = mgh = 1 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 5 \, \text{m} = 49.05 \, \text{J} \] ### Step 4: Conservation of Energy According to the principle of conservation of energy, the total mechanical energy (sum of potential and kinetic energy) remains constant if we neglect air resistance. Therefore, the initial potential energy at 10 m will equal the sum of the potential energy at 5 m and the kinetic energy at that height: \[ PE_{\text{initial}} = PE_{\text{5m}} + KE_{\text{5m}} \] Substituting the values we have: \[ 98.1 \, \text{J} = 49.05 \, \text{J} + KE_{\text{5m}} \] To find \( KE_{\text{5m}} \): \[ KE_{\text{5m}} = 98.1 \, \text{J} - 49.05 \, \text{J} = 49.05 \, \text{J} \] ### Step 5: Comparing Kinetic Energy to Initial Potential Energy Now, we need to compare the kinetic energy at 5 m to the initial potential energy: - Initial potential energy \( PE_{\text{initial}} = 98.1 \, \text{J} \) - Kinetic energy at 5 m \( KE_{\text{5m}} = 49.05 \, \text{J} \) ### Step 6: Analyzing the Options Now, let's analyze the options provided: - **Option A: Its kinetic energy on the ground** This is incorrect because the kinetic energy on the ground would be maximum, equal to the initial potential energy (98.1 J), not the kinetic energy at 5 m. - **Option B: Twice its initial potential energy** This is incorrect because twice the initial potential energy would be \( 2 \times 98.1 \, \text{J} = 196.2 \, \text{J} \), which is not the kinetic energy at 5 m. - **Option C: Its initial potential energy** This is incorrect because the kinetic energy at 5 m (49.05 J) is not equal to the initial potential energy (98.1 J). - **Option D: Half its initial potential energy** This is correct because half of the initial potential energy is: \[ \frac{98.1 \, \text{J}}{2} = 49.05 \, \text{J} \] which matches the kinetic energy at 5 m. ### Conclusion The correct answer is **D: half its initial potential energy**. ### Revision Summary - The potential energy at a height is calculated using \( PE = mgh \). - The kinetic energy is derived from the conservation of energy principle. - At 5 m, the kinetic energy is equal to half of the initial potential energy. - Always compare energies at different heights to understand the energy transformations in free fall.