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Rocket motion - Maximum height reached

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A rocket is fired vertically upwards with initial speed V and is propelled by ejecting material downwards at a constant rate and with a constant speed u relative to the rocket. After a time T the propellant material is exhausted and the rocket still rising. Neglecting air resistance, show that the maximum height h attained is given by 2gh = (u ln )^2 - 2Vu ln +V^2+2guT[1+ln /(1- )] where is the ratio of the mass of the rocket alone to the total initial mass of the rocket and propellant

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