To determine which rocket has the highest acceleration, we need to use Newton's second law of motion, which states that acceleration ([tex]\(a\)[/tex]) is equal to the net force ([tex]\(F\)[/tex]) divided by the mass ([tex]\(m\)[/tex]) of the object. Mathematically, this is given by the formula:
[tex]\[ a = \frac{F}{m} \][/tex]
We will calculate the acceleration for each rocket using the given masses and the net force of [tex]\(120 \, \text{N}\)[/tex].
Step-by-Step Calculation:
1. Rocket 1:
[tex]\[ m = 4.25 \, \text{kg}, \, F = 120 \, \text{N} \][/tex]
[tex]\[ a = \frac{120 \, \text{N}}{4.25 \, \text{kg}} \][/tex]
[tex]\[ a \approx 28.235 \, \text{m/s}^2 \][/tex]
2. Rocket 2:
[tex]\[ m = 3.25 \, \text{kg}, \, F = 120 \, \text{N} \][/tex]
[tex]\[ a = \frac{120 \, \text{N}}{3.25 \, \text{kg}} \][/tex]
[tex]\[ a \approx 36.923 \, \text{m/s}^2 \][/tex]
3. Rocket 3:
[tex]\[ m = 5.50 \, \text{kg}, \, F = 120 \, \text{N} \][/tex]
[tex]\[ a = \frac{120 \, \text{N}}{5.50 \, \text{kg}} \][/tex]
[tex]\[ a \approx 21.818 \, \text{m/s}^2 \][/tex]
4. Rocket 4:
[tex]\[ m = 4.50 \, \text{kg}, \, F = 120 \, \text{N} \][/tex]
[tex]\[ a = \frac{120 \, \text{N}}{4.50 \, \text{kg}} \][/tex]
[tex]\[ a \approx 26.667 \, \text{m/s}^2 \][/tex]
Comparison of Accelerations:
- Rocket 1: [tex]\( 28.235 \, \text{m/s}^2 \)[/tex]
- Rocket 2: [tex]\( 36.923 \, \text{m/s}^2 \)[/tex]
- Rocket 3: [tex]\( 21.818 \, \text{m/s}^2 \)[/tex]
- Rocket 4: [tex]\( 26.667 \, \text{m/s}^2 \)[/tex]
From the calculated values, we can see that the highest acceleration is [tex]\(36.923 \, \text{m/s}^2 \)[/tex], which belongs to Rocket 2.
Conclusion:
The rocket with the highest acceleration is Rocket 2. Therefore, the correct answer is:
- A. Rocket 2
