To understand how to achieve the goal of the second rocket accelerating at half the rate of the first, we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
For the first rocket:
- Mass (\( m_1 \)) = 0.2 kg
- Force (\( F \)) = 100 N
- Acceleration (\( a_1 \)) can be calculated as follows:
\[ a_1 = \frac{F}{m_1} = \frac{100 , \text{N}}{0.2 , \text{kg}} = 500 , \text{m/s}^2 \]
The second rocket is required to accelerate at half this rate, so:
\[ a_2 = \frac{a_1}{2} = \frac{500 , \text{m/s}^2}{2} = 250 , \text{m/s}^2 \]
Using the same force of 100 N for the second rocket, we can find the required mass (\( m_2 \)):
\[ F = m_2 \cdot a_2 \Rightarrow m_2 = \frac{F}{a_2} = \frac{100 , \text{N}}{250 , \text{m/s}^2} = 0.4 , \text{kg} \]
This calculation shows that to achieve half the acceleration of the first rocket with the same motor force, the mass of the second rocket should be 0.4 kg.
Therefore, the correct option is:
The mass of the second rocket should be 0.4 kg.
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