Question

A rocket has a mass of 0.8 kg and an engine that provides 100 N of force. A second rocket is being designed to use the same engine but accelerate at half the rate of the first rocket. What is the mass of the second rocket?


a
0.4 kg
b
1.6 kg
c
2.4 kg
d
0.8 kg

Answer 1

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:

1. For the first rocket, which has a mass of 0.8 kg:

\[ a_1 = \frac{F}{m_1} = \frac{100 \text{ N}}{0.8 \text{ kg}} = 125 \text{ m/s}^2 \]

2. The second rocket is designed to accelerate at half this rate:

\[ a_2 = \frac{a_1}{2} = \frac{125 \text{ m/s}^2}{2} = 62.5 \text{ m/s}^2 \]

3. 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**