Calculate the gravitational force of attraction …

To calculate the gravitational force of attraction between the stone and the Earth and the accelerations produced, we can use Newton's law of universal gravitation: \[F = \frac{{G \cdot (m1 \cdot m2)}}{{r^2}}\] Where: - \(F\) is the gravitational force of attraction between the two objects. - \(G\) is the gravitational constant, which is approximately \(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2\). - \(m1\) is the mass of the stone, which is 1 kilogram (\(1 \, \text{kg}\)). - \(m2\) is the mass of the Earth, which is \(6 \times 10^{24} \, \text{kg}\). - \(r\) is the distance between the center of the Earth and the stone, which is the radius of the Earth plus the height at which the stone is located. First, let's convert the radius of the Earth from kilometers to meters: \[r = 6.4 \times 10^6 \, \text{km} = 6.4 \times 10^6 \times 1000 \, \text{m} = 6.4 \times 10^9 \, \text{m}\] Now, we can calculate the gravitational force of attraction between the stone and the Earth: \[F = \frac{{6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \cdot (1 \, \text{kg} \cdot 6 \times 10^{24} \, \text{kg})}}{{(6.4 \times 10^9 \, \text{m})^2}}\] Calculating this expression will give us the gravitational force of attraction (\(F\)) between the stone and the Earth. The acceleration produced in the stone (\(a_{\text{stone}}\)) can be found using Newton's second law (\(F = m \cdot a\)), and the acceleration produced in the Earth (\(a_{\text{Earth}}\)) can be calculated using the same formula, considering the mass of the Earth. Let's calculate \(F\), \(a_{\text{stone}}\), and \(a_{\text{Earth}}\).