A rocket of initial mass `6000kg` ejects mass at a constant rate of `16kg//s` with constant relative speed of `11m//s` What is the acceleration of the rocket one mnute after blast ?

Options

A. `25"ms"^(-2)`
B. `50"ms"^(-2)`
C. `10"ms"^(-2)`
D. `35"ms"^(-2)`

Explanation

To solve the problem of finding the acceleration of the rocket one minute after the blast, we can follow these steps:

### Step 1: Determine the initial mass of the rocket.
The initial mass \( m_0 \) of the rocket is given as:
\[ m_0 = 6000 \, \text{kg} \]

### Step 2: Calculate the mass of the rocket after one minute.
The rocket ejects mass at a constant rate of \( \frac{dm}{dt} = 16 \, \text{kg/s} \). We need to find the total mass ejected in one minute (60 seconds):
\[ \text{Mass ejected} = \frac{dm}{dt} \times \text{time} = 16 \, \text{kg/s} \times 60 \, \text{s} = 960 \, \text{kg} \]
Now, we can find the mass of the rocket after one minute:
\[ m = m_0 - \text{Mass ejected} = 6000 \, \text{kg} - 960 \, \text{kg} = 5040 \, \text{kg} \]

### Step 3: Determine the relative speed of the ejected mass.
The relative speed \( V \) of the ejected mass is given as:
\[ V = 11 \, \text{m/s} \]

### Step 4: Calculate the thrust force.
The thrust force \( F \) generated by the rocket can be calculated using the formula:
\[ F = \frac{dm}{dt} \times V \]
Substituting the values:
\[ F = 16 \, \text{kg/s} \times 11 \, \text{m/s} = 176 \, \text{N} \]

### Step 5: Calculate the acceleration of the rocket.
Using Newton's second law, the acceleration \( a \) of the rocket can be calculated as:
\[ a = \frac{F}{m} \]
Substituting the thrust force and the mass of the rocket after one minute:
\[ a = \frac{176 \, \text{N}}{5040 \, \text{kg}} \approx 0.0349 \, \text{m/s}^2 \]

### Step 6: Final Result
Thus, the acceleration of the rocket one minute after the blast is approximately:
\[ a \approx 0.0349 \, \text{m/s}^2 \]