To determine which combination of rocket bodies and engines will result in an acceleration of [tex]\( 40 \, \text{m/s}^2 \)[/tex] at the start of the launch, we can use Newton's second law of motion, which states:
[tex]\[ F = m \cdot a \][/tex]
Where:
- [tex]\( F \)[/tex] is the force in Newtons (N)
- [tex]\( m \)[/tex] is the mass in kilograms (kg)
- [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\(\text{m/s}^2\)[/tex])
We can rearrange this equation to solve for acceleration:
[tex]\[ a = \frac{F}{m} \][/tex]
We need to check each combination of rocket body and engine to see if the acceleration is [tex]\( 40 \, \text{m/s}^2 \)[/tex].
### Combinations to Check
1. Body 1 (mass = 0.500 kg) + Engine 1 (force = 25 N):
[tex]\[
a = \frac{25 \, \text{N}}{0.500 \, \text{kg}} = 50 \, \text{m/s}^2
\][/tex]
2. Body 2 (mass = 1.5 kg) + Engine 2 (force = 20 N):
[tex]\[
a = \frac{20 \, \text{N}}{1.5 \, \text{kg}} = \frac{20}{1.5} = 13.33 \, \text{m/s}^2
\][/tex]
3. Body 3 (mass = 0.750 kg) + Engine 3 (force = 30 N):
[tex]\[
a = \frac{30 \, \text{N}}{0.750 \, \text{kg}} = 40 \, \text{m/s}^2
\][/tex]
4. Body 1 (mass = 0.500 kg) + Engine 2 (force = 20 N):
[tex]\[
a = \frac{20 \, \text{N}}{0.500 \, \text{kg}} = 40 \, \text{m/s}^2
\][/tex]
### Suitable Combinations
Based on the calculations:
- Body 3 + Engine 3 results in an acceleration of [tex]\( 40 \, \text{m/s}^2 \)[/tex].
- Body 1 + Engine 2 also results in an acceleration of [tex]\( 40 \, \text{m/s}^2 \)[/tex].
Hence, the suitable combinations that result in an acceleration of [tex]\( 40 \, \text{m/s}^2 \)[/tex] at the start of the launch are:
- Body 3 + Engine 3
- Body 1 + Engine 2
