Question

A rocket with a lift-off mass $3.5\times {10}^{4}kg$ is blasted upwards with an initial acceleration of $10m/s^2$. The initial thrust of the blast is:

Answer 1

Given data

1. The mass of the rocket is $m=3.5\times {10}^{4}kg$
2. Acceleration of blast is $a=10m/s^2$

Rocket thrust

1. Rocket thrust is a reaction force on the rocket due to the outflow of rocket fuel at a very high speed.
2. Due to this thrust rocket moves in space.

Diagram

Calculation of initial rocket thrust

Now, the net force exerted on the rocket is $F=F_t-mg$, where, $F_t$ is the upward thrust on the rocket.

Now, the initial thrust is

$$\begin{gathered} F_t=F+mg=ma+mg \\ or{F}_t=m(a+g)=\left(3.5\times {10}^4\right)\times \left(9.8+10\right) \\ or{F}_t=\left(3.5\times {10}^4\right)\times 19.8 \\ or{F}_t=6.9\times {10}^{5}N. \end{gathered}$$

Therefore, The initial thrust of the blast is $6.9\times {10}^{5}N$