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A rocket in deep space moving with velocity of 300 m/s has an initial mass of...

A rocket in deep space moving with velocity of 300 m/s has an initial mass of 5000 kg, of which 2000 kg are fuel. If it is ejecting gasses at a rate of 5 kg/s at a speed of 200 m/s relative to the rocket, then after 200 second of motion, its speed is

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Answer #1

Let the speed of the rocket after 200 s is v.

The initial velocity u=300 m/s.

The speed of the gasses V=200 m/s.

The rate of ejecting gasses is 5 kg/s.

The total initial mass of the rocket is 5000 kg.

The mass of the fuel is 2000 kg.

Mass of the rocket after 200 s is

  

We know

  

  

The velocity of the rocket after 200 seconds is 344.629 m/s.

  

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