The center of mass of the two objects is the average position of the parts of the two object system
The center of mass of block <em>A</em>, and block <em>B</em> after displacement of block <em>B</em> is at <u>20 m from block </u><u><em>A</em></u>
<em />
Reason:
The given parameters are;
The position of block A and block B at t = 0 is x = 0
The mass of block A, m₁ = 8 kg
Mass of block B, m₂ = 16 kg
Speed of block <em>A</em> = 0 m/s
Speed of block <em>B</em>, v₂ = 10 m/s
Location of the center of mass of the two object at t = 3 s; Required
Solution;
The location of block <em>A</em>, after 3 s is x₁ = 0 (block A is at rest)
The location of block <em>B</em>, = v₂ × t
The location of block <em>B</em>, after 3 s is x₂ = 10 m/s × 3 s = 30 m
The center of mass of two masses are given as follows;
![x_{cm} = \dfrac{m_1 \cdot x_1 +m_2\cdot x_2}{m_1 + m_2}](https://tex.z-dn.net/?f=x_%7Bcm%7D%20%3D%20%5Cdfrac%7Bm_1%20%5Ccdot%20x_1%20%2Bm_2%5Ccdot%20x_2%7D%7Bm_1%20%2B%20m_2%7D)
![x_{cm} = \dfrac{8 \times0 + 16 \times 30}{8 + 16} = 20](https://tex.z-dn.net/?f=x_%7Bcm%7D%20%3D%20%5Cdfrac%7B8%20%20%5Ctimes0%20%2B%2016%20%5Ctimes%20%2030%7D%7B8%20%2B%2016%7D%20%3D%2020)
The center of mass of the two objects is at at the position x = <u>20 m</u> (from block <em>A</em>)
Learn more about the center of mass here:
brainly.com/question/18557256
brainly.com/question/20714030
brainly.com/question/17088562