Given:
Mass of rocket (m) = 1000 kg
Rate of fuel consumption (dm/dt) = 40 kg/s
Velocity of ejected gases (v) = 5 * 10^4 m/s

To Find:
Thrust on the rocket

Solution:

1. Conservation of Momentum:
According to the principle of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it. In this case, the rocket and the ejected gases form an isolated system.

2. Initial Momentum:
Before the fuel is consumed, the rocket is at rest, so its initial momentum (p_initial) is zero.

Initial momentum (p_initial) = 0 kg m/s

3. Final Momentum:
After the fuel is consumed, the rocket starts moving due to the ejection of gases. The final momentum (p_final) of the system can be calculated using the equation:

Final momentum (p_final) = (Mass of rocket + Mass of ejected gases) * Velocity of rocket

The mass of ejected gases can be calculated using the equation:

Mass of ejected gases (dm_ejected) = Rate of fuel consumption (dm/dt) * Time (dt)

4. Time Interval:
To calculate the mass of ejected gases, we need to determine the time interval (dt). As the fuel consumption rate is given in kg/s, we can assume a small time interval (dt) of 1 second.

Time interval (dt) = 1 s

5. Mass of Ejected Gases:
Using the time interval and rate of fuel consumption, the mass of ejected gases can be calculated.

Mass of ejected gases (dm_ejected) = Rate of fuel consumption (dm/dt) * Time interval (dt)
dm_ejected = 40 kg/s * 1 s
dm_ejected = 40 kg

6. Final Momentum:
Using the mass of the rocket and the mass of ejected gases, we can calculate the final momentum.

Final momentum (p_final) = (Mass of rocket + Mass of ejected gases) * Velocity of rocket
p_final = (1000 kg + 40 kg) * (5 * 10^4 m/s)
p_final = 1.02 * 10^8 kg m/s

7. Thrust:
The thrust on the rocket is equal to the rate of change of momentum, which can be calculated using the equation:

Thrust = Final momentum (p_final) - Initial momentum (p_initial)

As the initial momentum is zero, the thrust on the rocket is equal to the final momentum.

Thrust = 1.02 * 10^8 kg m/s

Answer:
The thrust on the rocket is 1.02 * 10^8 kg m/s.

F=udm/dt

=40×5*10^4=2×10^6