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 ?

Explanation

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

### Step 1: Calculate the mass of the rocket after one minute
The initial mass of the rocket is given as \( m_0 = 6000 \, \text{kg} \). The rocket ejects mass at a constant rate of \( \frac{dm}{dt} = 16 \, \text{kg/s} \).

After one minute (which is 60 seconds), the total mass ejected is:
\[ \text{Mass ejected} = \frac{dm}{dt} \times \text{time} = 16 \, \text{kg/s} \times 60 \, \text{s} = 960 \, \text{kg} \]

Thus, the mass of the rocket after one minute is:
\[ m = m_0 - \text{Mass ejected} = 6000 \, \text{kg} - 960 \, \text{kg} = 5040 \, \text{kg} \]

### Step 2: Calculate the thrust force of the rocket
The thrust force \( F \) generated by the rocket is given by the formula:
\[ F = \frac{dm}{dt} \times v \]
where \( v \) is the relative speed of the ejected mass. In this case, \( v = 11 \, \text{m/s} \).

Substituting the values:
\[ F = 16 \, \text{kg/s} \times 11 \, \text{m/s} = 176 \, \text{N} \]

### Step 3: 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 values we have:
\[ a = \frac{176 \, \text{N}}{5040 \, \text{kg}} \approx 0.03492 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the rocket one minute after the blast is approximately \( 0.03492 \, \text{m/s}^2 \).

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