Force and acceleration of a rocket

[Sarah0001]

Homework Statement

A rocket, total mass 1.00 × 10^4 kg, is launched vertically; eighty per cent of the mass being fuel. At ignition, time t = 0, the thrust equals the weight of the rocket. The ejected exhaust gases have a speed of 9.00 × 10^2 ms ^–1. Assuming the rate of fuel consumption and the acceleration due to gravity are constant,

calculate: (i) the mass, m, of gases ejected per second (ii) the acceleration, a_e , of the rocket when the fuel is almost exhausted at time t_e

The part I am stuck on is part ii - I am confused on how the thrust is equal to 1.00 × 10^4 * g as seen on the uploaded work solutions below.
F net = Thrust - Weight of rocket
Total Mass of rocket * net acceleration = Thrust - 0.2* total mass rocket *acceleration due to gravity
I am confused on how the Thrust is equal to the weight of the total mass of the rocket. Is there a physical explanation for this

Homework Equations

F=ma
W = Mg

3. My attempt at a solution
Am I correct in my logic that since the exhaust gases cause the thrust of the rocket, then

the net acceleration of the rocket would be the mass of the exhaust gases at time t_e multiplied by acceleration due to gravity and this product divided by the mass of the rocket, as this is what the thrust force is acting on.

Although this gets to the same numerical answer, I am not convinced I used Newton's Second Law in terms of the worked solutions as I am currently unable to understand how thrust at that time where fuel is nearly exhausted, equals 1.00*10^4 *g. I just thought that thrust equals the exhaust gases * g , and acting on the rocket. I feel there is something wrong in my understanding.

 

[haruspex]

am confused on how the thrust is equal to 1.00 × 10^4 * g

You are given this:

At ignition, time t = 0, the thrust equals the weight of the rocket.

That is, at ignition there is no acceleration. But as fuel burns the weight goes down and the thrust exceeds the weight.

the net acceleration of the rocket would be the mass of the exhaust gases at time

The thrust comes from the expulsion of the exhaust. This depends on the rate of ejection of fuel mass and the speed at which it is ejected.

multiplied by acceleration due to gravity

How can gravity contribute to thrust?!

 

[Sarah0001]

[/QUOTE]That is, at ignition there is no acceleration. But as fuel burns the weight goes down and the thrust exceeds the weight.

The thrust comes from the expulsion of the exhaust. This depends on the rate of ejection of fuel mass and the speed at which it is ejected.

You are given this:
Thank you

Since both the speed at which it is ejected is constant (9.00*10^2 ms^-1), and as the rate of ejection of fuel is constant too (which is in Kg s^1 ?) does this mean we can assume the thrust to be constant from t=0 throughout the duration of the flight?

 

[haruspex]

Since both the speed at which it is ejected is constant (9.00*10^2 ms^-1), and as the rate of ejection of fuel is constant too (which is in Kg s^1 ?) does this mean we can assume the thrust to be constant from t=0 throughout the duration of the flight?

Yes.