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A rocket accelerates straight up by ejec...

A rocket accelerates straight up by ejecting gas downwards. In a small time interval `Deltat`, it ejects a gas of mass `Delta m` at a relative speed `u` . Calculate KE of the entire system at `t+Deltat` and `t` and show that the device that ejects gas does work `=((1)/(2))Delta m . u^(2)` in this time interval (neglect gavity).

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