To find the mass of the second rocket, we can use Newton's second law of motion, which states:
\[ F = m \times a \]
Where:
- \( F \) is the force provided (100 N in this case),
- \( m \) is the mass,
- \( a \) is the acceleration.
First, we calculate the acceleration of the first rocket:
- For the first rocket, which has a mass of 0.8 kg:
\[ a_1 = \frac{F}{m_1} = \frac{100 \text{ N}}{0.8 \text{ kg}} = 125 \text{ m/s}^2 \]
- The second rocket is designed to accelerate at half this rate:
\[ a_2 = \frac{a_1}{2} = \frac{125 \text{ m/s}^2}{2} = 62.5 \text{ m/s}^2 \]
- Now we can find the mass of the second rocket using the same force:
Using the equation again for the second rocket:
\[ F = m_2 \times a_2 \]
Rearranging for \( m_2 \):
\[ m_2 = \frac{F}{a_2} = \frac{100 \text{ N}}{62.5 \text{ m/s}^2} = 1.6 \text{ kg} \]
So, the mass of the second rocket is 1.6 kg. The correct option is:
b. 1.6 kg