A rocket of mass 120kg. Is fired in the gravity free space is ejected gases with velocity 600 m/s at the rate of 1kg/s. what will be the initial accleration of the rocket:-

Options

A. `1m//s^(2)`
B. `5m//s^(2)`
C. `10m//s^(2)`
D. `15m//s^(2)`

Explanation

To find the initial acceleration of the rocket, we can use the thrust force generated by the ejection of gases and apply Newton's second law of motion. Here are the steps to solve the problem:

### Step 1: Identify the given values
- Mass of the rocket (m) = 120 kg
- Velocity of ejected gases (v_r) = 600 m/s
- Rate of mass ejection (dm/dt) = 1 kg/s

### Step 2: Calculate the thrust force (F_thrust)
The thrust force can be calculated using the formula:
\[ F_{\text{thrust}} = v_r \cdot \frac{dm}{dt} \]
Substituting the known values:
\[ F_{\text{thrust}} = 600 \, \text{m/s} \cdot 1 \, \text{kg/s} = 600 \, \text{N} \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force acting on the rocket is equal to the mass of the rocket multiplied by its acceleration (a):
\[ F_{\text{net}} = m \cdot a \]
Since the thrust force is the only force acting on the rocket (in the absence of gravity), we can set the thrust force equal to the net force:
\[ F_{\text{thrust}} = m \cdot a \]
Substituting the values we have:
\[ 600 \, \text{N} = 120 \, \text{kg} \cdot a \]

### Step 4: Solve for acceleration (a)
Rearranging the equation to solve for acceleration:
\[ a = \frac{F_{\text{thrust}}}{m} = \frac{600 \, \text{N}}{120 \, \text{kg}} = 5 \, \text{m/s}^2 \]

### Conclusion
The initial acceleration of the rocket is:
\[ a = 5 \, \text{m/s}^2 \]