To determine the mass of the second rocket needed to achieve half the acceleration of the first rocket, we can use Newton's second law, \( F = ma \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration.
First, we calculate the acceleration of the first rocket. Given:
- Mass of the first rocket, \( m_1 = 0.2 \) kg
- Force provided by the motor, \( F = 100 \) N
Using the equation, the acceleration \( a_1 \) of the first rocket is given by: \[ a_1 = \frac{F}{m_1} = \frac{100 \text{ N}}{0.2 \text{ kg}} = 500 \text{ m/s}^2 \]
The second rocket is designed to accelerate half as much: \[ a_2 = \frac{1}{2} a_1 = \frac{1}{2} \times 500 \text{ m/s}^2 = 250 \text{ m/s}^2 \]
Now, we use the same force (100 N) to find the mass of the second rocket, \( m_2 \), which will give us the desired acceleration: \[ F = m_2 \cdot a_2 \] \[ 100 \text{ N} = m_2 \cdot 250 \text{ m/s}^2 \] \[ m_2 = \frac{100 \text{ N}}{250 \text{ m/s}^2} = 0.4 \text{ kg} \]
Thus, to achieve half the acceleration, the mass of the second rocket should be 0.4 kg.
The correct answer is: The mass of the second rocket should be 0.4 kg.
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