To determine the gravitational force between the semitruck and the car, we'll use Newton's law of universal gravitation. The formula for the gravitational force [tex]\( F \)[/tex] is given by:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant, [tex]\( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)[/tex],
- [tex]\( m_1 \)[/tex] is the mass of the semitruck, [tex]\( 20{,}000 \, \text{kg} \)[/tex],
- [tex]\( m_2 \)[/tex] is the mass of the car, [tex]\( 2{,}000 \, \text{kg} \)[/tex],
- [tex]\( r \)[/tex] is the distance between the semitruck and the car, [tex]\( 10 \, \text{m} \)[/tex].
Let's plug in the given values into the formula:
1. Calculate the product of the masses:
[tex]\[ m_1 \cdot m_2 = 20{,}000 \, \text{kg} \times 2{,}000 \, \text{kg} = 40{,}000{,}000 \, \text{kg}^2 \][/tex]
2. Calculate the square of the distance:
[tex]\[ r^2 = (10 \, \text{m})^2 = 100 \, \text{m}^2 \][/tex]
3. Plug these values and [tex]\( G \)[/tex] into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \cdot \frac{40{,}000{,}000}{100} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{40{,}000{,}000}{100} = 400{,}000 \][/tex]
5. Multiply by the gravitational constant [tex]\( G \)[/tex]:
[tex]\[ F = 6.67 \times 10^{-11} \cdot 400{,}000 \][/tex]
[tex]\[ F = 2.668 \times 10^{-5} \, \text{N} \][/tex]
Thus, the gravitational force between the semitruck and the car is approximately [tex]\( 2.67 \times 10^{-5} \, \text{N} \)[/tex].
Therefore, the correct answer is:
C. [tex]\( 2.67 \times 10^{-5} \, \text{N} \)[/tex]
