To determine the mass of the second rocket to achieve half the acceleration of the first rocket, we can use Newton's second law, which states that \( F = ma \) (where \( F \) is force, \( m \) is mass, and \( a \) is acceleration).
For the first rocket:
- Mass \( m_1 = 0.2 , \text{kg} \)
- Force \( F = 100 , \text{N} \)
The acceleration \( a_1 \) of the first rocket can be calculated as: \[ a_1 = \frac{F}{m_1} = \frac{100 , \text{N}}{0.2 , \text{kg}} = 500 , \text{m/s}^2 \]
For the second rocket, we want it to accelerate half as much, so: \[ a_2 = \frac{a_1}{2} = \frac{500 , \text{m/s}^2}{2} = 250 , \text{m/s}^2 \]
Using the same force of \( 100 , \text{N} \) for the second rocket, we can find the mass \( m_2 \): \[ m_2 = \frac{F}{a_2} = \frac{100 , \text{N}}{250 , \text{m/s}^2} = 0.4 , \text{kg} \]
Therefore, to achieve half the acceleration of the first rocket, the mass of the second rocket should be 0.4 kg.
The correct response is: The mass of the second rocket should be 0.4 kg.