The rate of mass of the gas emitted from the rear of a rocket is initially `0.1 kg//s`. If the speed of the gas relative to the rocket is `50 m//s` and the mass of the rocket is `2 kg` , then the acceleration of the rocket in `m//s^(2)` is

Options

A. `5`
B. `5.2`
C. `2.5`
D. `25`

Explanation

To find the acceleration of the rocket, we can follow these steps:

### Step 1: Identify the given values
- Rate of mass emitted from the rocket (\( \frac{dm}{dt} \)) = 0.1 kg/s
- Speed of the gas relative to the rocket (\( V_r \)) = 50 m/s
- Mass of the rocket (\( m \)) = 2 kg

### Step 2: Calculate the thrust force (\( F_t \))
The thrust force can be calculated using the formula:
\[ F_t = \frac{dm}{dt} \cdot V_r \]
Substituting the values:
\[ F_t = 0.1 \, \text{kg/s} \cdot 50 \, \text{m/s} = 5 \, \text{N} \]

### Step 3: Use Newton's second law to find acceleration
According to Newton's second law:
\[ F = m \cdot a \]
We can rearrange this to find acceleration (\( a \)):
\[ a = \frac{F}{m} \]
Substituting the thrust force and the mass of the rocket:
\[ a = \frac{5 \, \text{N}}{2 \, \text{kg}} = 2.5 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the rocket is \( 2.5 \, \text{m/s}^2 \).

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