A rocket with a lift-off mass `3.5xx10^4 kg` is blasted upwards with an initial acceleration of `10m//s^2`. Then the initial thrust of the blast is

Options

A. `3.5xx10^(5) N`
B. `7.0xx10^(5)N`
C. `14.0xx10^(5)N`
D. `1.75xx10^(5)N`

Explanation

To find the initial thrust of the rocket, we can use Newton's second law of motion. The thrust must overcome both the force of gravity acting on the rocket and provide the necessary force for the upward acceleration.

### Step-by-Step Solution:

1. **Identify the given values:**
- Lift-off mass of the rocket, \( m = 3.5 \times 10^4 \, \text{kg} \)
- Acceleration of the rocket, \( a = 10 \, \text{m/s}^2 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Calculate the force of gravity acting on the rocket:**
\[ F_g = m \cdot g \]
Substituting the values:
\[ F_g = 3.5 \times 10^4 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 3.5 \times 10^5 \, \text{N} \]

3. **Calculate the total force required for the upward acceleration:**
The total force (thrust) required is the sum of the force of gravity and the force needed for the upward acceleration:
\[ F_{\text{thrust}} = F_g + F_a \]
where \( F_a = m \cdot a \).

4. **Calculate the force needed for the upward acceleration:**
\[ F_a = m \cdot a = 3.5 \times 10^4 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 3.5 \times 10^5 \, \text{N} \]

5. **Combine the forces to find the thrust:**
\[ F_{\text{thrust}} = F_g + F_a = 3.5 \times 10^5 \, \text{N} + 3.5 \times 10^5 \, \text{N} = 7.0 \times 10^5 \, \text{N} \]

6. **Conclusion:**
The initial thrust of the rocket is \( 7.0 \times 10^5 \, \text{N} \).

### Final Answer:
The initial thrust of the rocket is \( 7.0 \times 10^5 \, \text{N} \).

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