Paper 4, Section I, A

Dynamics and Relativity | Part IA, 2019

A rocket of mass m(t)m(t) moving at speed v(t)v(t) and ejecting fuel behind it at a constant speed uu relative to the rocket, is subject to an external force FF. Considering a small time interval δt\delta t, derive the rocket equation

mdvdt+udmdt=Fm \frac{d v}{d t}+u \frac{d m}{d t}=F

In deep space where F=0F=0, how much faster does the rocket go if it burns half of its mass in fuel?

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