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 principles of momentum and Newton's second law of motion. Here’s a step-by-step solution:

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

### Step 2: Calculate the thrust produced by the rocket
The thrust (F) produced by the rocket can be calculated using the formula:
\[ F = \frac{dm}{dt} \times v \]
Where:
- \( \frac{dm}{dt} \) is the rate of mass ejection.
- \( v \) is the velocity of the ejected gases.

Substituting the values:
\[ F = 1 \, \text{kg/s} \times 600 \, \text{m/s} = 600 \, \text{N} \]

### Step 3: Apply Newton's second law to find acceleration
According to Newton's second law:
\[ F = m \times a \]
Where:
- \( F \) is the thrust (600 N).
- \( m \) is the mass of the rocket (120 kg).
- \( a \) is the acceleration we want to find.

Rearranging the formula to solve for acceleration \( a \):
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{600 \, \text{N}}{120 \, \text{kg}} = 5 \, \text{m/s}^2 \]

### Step 4: Conclusion
The initial acceleration of the rocket is \( 5 \, \text{m/s}^2 \).

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