Find the relationship between the mass of the rocket m(t), the speed v(t) it achieves and the time t, if the rocket moves vertically upward in the Earth’s gravitational field. The speed of the gas jet relative to the rocket u is considered constant. Ignore air resistance and changes in gravitational acceleration g with height. What mass of gases m(t) must the rocket eject every second in order to remain motionless relative to the Earth?

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