In the first second of its flight a rocket ejects `(1)/(60)` of its mass with a reative velocity `2073ms^(-1)` What is the initial acceleration of the rocket ? .

Explanation

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

### Step 1: Identify the mass ejected and the thrust force
The rocket ejects \( \frac{1}{60} \) of its mass in the first second. Let's denote the total mass of the rocket as \( m \). Therefore, the mass ejected in the first second is:
\[ \Delta m = \frac{m}{60} \]

The velocity of the ejected mass is given as \( v = 2073 \, \text{m/s} \).

### Step 2: Calculate the thrust force
The thrust force \( F_t \) can be calculated using the formula:
\[ F_t = \frac{dm}{dt} \cdot v \]
Here, \( \frac{dm}{dt} \) is the rate of mass ejection. Since the rocket ejects \( \frac{m}{60} \) in 1 second, we have:
\[ \frac{dm}{dt} = \frac{m}{60} \, \text{kg/s} \]
Substituting this into the thrust force equation:
\[ F_t = \left(\frac{m}{60}\right) \cdot 2073 \]
\[ F_t = \frac{2073m}{60} \]

### Step 3: Write the net force equation
The net force acting on the rocket can be expressed as:
\[ F_{\text{net}} = F_t - mg \]
where \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)). Therefore:
\[ F_{\text{net}} = \frac{2073m}{60} - mg \]

### Step 4: Apply Newton's second law
According to Newton's second law:
\[ F_{\text{net}} = ma \]
Substituting the expression for net force:
\[ ma = \frac{2073m}{60} - mg \]

### Step 5: Simplify the equation
We can cancel \( m \) from both sides (assuming \( m \neq 0 \)):
\[ a = \frac{2073}{60} - g \]
Substituting \( g = 10 \, \text{m/s}^2 \):
\[ a = \frac{2073}{60} - 10 \]

### Step 6: Calculate the value of acceleration
First, calculate \( \frac{2073}{60} \):
\[ \frac{2073}{60} \approx 34.55 \]
Now substituting this back into the equation for acceleration:
\[ a = 34.55 - 10 = 24.55 \, \text{m/s}^2 \]

### Final Answer
The initial acceleration of the rocket is:
\[ \boxed{24.55 \, \text{m/s}^2} \]