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]) acting on the object divided by the object's mass ([tex]\( m \)[/tex]). Mathematically, it is represented as:
[tex]\[ a = \frac{F}{m} \][/tex]
Given:
- The net force ([tex]\( F \)[/tex]) on each rocket is 120 N.
- The masses of the rockets are as follows:
- Rocket 1: 4.25 kg
- Rocket 2: 3.25 kg
- Rocket 3: 5.50 kg
- Rocket 4: 4.50 kg
We'll calculate the acceleration for each rocket individually.
Rocket 1:
[tex]\[ a_1 = \frac{120 \, \text{N}}{4.25 \, \text{kg}} = 28.24 \, \text{m/s}^2 \][/tex]
Rocket 2:
[tex]\[ a_2 = \frac{120 \, \text{N}}{3.25 \, \text{kg}} = 36.92 \, \text{m/s}^2 \][/tex]
Rocket 3:
[tex]\[ a_3 = \frac{120 \, \text{N}}{5.50 \, \text{kg}} = 21.82 \, \text{m/s}^2 \][/tex]
Rocket 4:
[tex]\[ a_4 = \frac{120 \, \text{N}}{4.50 \, \text{kg}} = 26.67 \, \text{m/s}^2 \][/tex]
Next, we compare the accelerations calculated:
- Rocket 1: [tex]\( 28.24 \, \text{m/s}^2 \)[/tex]
- Rocket 2: [tex]\( 36.92 \, \text{m/s}^2 \)[/tex]
- Rocket 3: [tex]\( 21.82 \, \text{m/s}^2 \)[/tex]
- Rocket 4: [tex]\( 26.67 \, \text{m/s}^2 \)[/tex]
The highest acceleration is [tex]\( 36.92 \, \text{m/s}^2 \)[/tex], which corresponds to Rocket 2.
Therefore, the rocket with the highest acceleration is:
B. Rocket 2
