To find the weight of the missile at an altitude using the inverse-square law of gravitation, we can use the formula for gravitational force: \(F = \frac{G \cdot m_1 \cdot m_2}{r^2}\) where: - \( F \) is the gravitational force (weight), - \( G \) is the gravitational constant, - \( m_1 \) is the mass of the Earth, - \( m_2 \) is the mass of the missile, - \( r \) is the distance from the center of the Earth to the missile. Step 1: Determine the radius at altitude 1. The radius of the Earth is \( R = 6.4 \times 10^6 \, \text{m} \). 2. The altitude \( h = 6.4 \times 10^6 \, \text{m} \). Thus, the distance from the center of the Earth to the missile at that altitude is: \(r = R + h = 6.4 \times 10^6 \, \text{m} + 6.4 \times 10^6 \, \text{m} = 12.8 \times 10^6 \, \text{m}\) Step 2: Calculate the weight at the altitude The weight of the missile at the surface is given as \( W_0 = 400 \, \text{N} \). The weight at altitude can be calculated using the ratio of the squares of the distances: \(W = W_0 \cdot \left( \frac{R}{r} \right)^2\) Substituting the values: \(W = 400 \cdot \left( \frac{6.4 \times 10^6}{12.8 \times 10^6} \right)^2\) Calculating this: \(W = 400 \cdot \left( \frac{1}{2} \right)^2 = 400 \cdot \frac{1}{4} = 100 \, \text{N}\) The weight of the missile at an altitude of \( 6.4 \times 10^6 \, \text{m} \) is \( 100 \, \text{N} \).