A rocket with a lift mass of 10,000 kg is blasted upwards with an acceleration of `10ms^(-2)`. Calculate the initial thrust of the blast

Answer

To calculate the initial thrust of the rocket, we need to consider both the force required to overcome gravity and the force required to accelerate the rocket upwards.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the rocket (m) = 10,000 kg
- Acceleration of the rocket (a) = 10 m/s²
- Acceleration due to gravity (g) = 9.8 m/s² (approximately)

2. **Calculate the Weight of the Rocket:**
The weight (W) of the rocket can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 10,000 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 98,000 \, \text{N} \]

3. **Calculate the Total Acceleration Required:**
To find the total acceleration that the thrust must overcome, we need to add the acceleration due to gravity to the upward acceleration of the rocket:
\[ \text{Total acceleration} = g + a = 9.8 \, \text{m/s}^2 + 10 \, \text{m/s}^2 = 19.8 \, \text{m/s}^2 \]

4. **Calculate the Thrust Force:**
The thrust force (T) required to lift the rocket can be calculated using Newton's second law:
\[ T = m \cdot \text{Total acceleration} \]
Substituting the values:
\[ T = 10,000 \, \text{kg} \cdot 19.8 \, \text{m/s}^2 = 198,000 \, \text{N} \]

5. **Final Result:**
The initial thrust of the blast is:
\[ T = 198,000 \, \text{N} \text{ or } 1.98 \times 10^5 \, \text{N} \]

### Summary:
The initial thrust of the rocket is **198,000 N** or **1.98 x 10^5 N**.