A rocket with a lift-off mass 3.5 x10⁴ kg is blasted upwards with an initial acceleration of 10 m / s². Then the initial thrust of the blast is

To find the initial thrust of the blast, we need to analyze the forces acting on the rocket at the moment of lift-off.

When the rocket is blasted upwards, two vertical forces act on it:
1. The upward thrust force, which we can denote as $F$.
2. The downward gravitational force (weight), which is given by $w=mg$, where $m$ is the mass of the rocket and $g$ is the acceleration due to gravity.

According to Newton's second law of motion, the net force acting on the rocket is equal to the product of its mass and its acceleration ($a$):

$F_{\text{net}}=F-mg=ma$

Rearranging this equation to solve for the upward thrust ($F$), we get:

$F=ma+mg=m(a+g)$

We are given the following values in the problem:
- Lift-off mass, $m=3.5\times {10}^4\text{kg}$
- Initial upward acceleration, $a=10{\text{m/s}}^2$
- Acceleration due to gravity, $g\approx 10{\text{m/s}}^2$

Substituting these values into the formula:

$F=(3.5\times {10}^4)\times (10+10)$

$F=(3.5\times {10}^4)\times 20$

$F=70\times {10}^4\text{N}$

$F=7.0\times {10}^5\text{N}$

Therefore, the initial thrust of the blast is $7.0\times {10}^5\text{N}$.