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A body consists of equal masses M of inflammable and non-inflammable material. The body descends freely under gravity from rest. The combustible part burns at a constant rate of kM per second where k is a constant. The burning material is ejected vertically upwards with constant speed u relative to the body, and air resistance may be neglected. Show, using momentum considerations, that d/dt[(2-kt)v]=k(u-v)+g(2-kt) where v is the speed of the body at time t. Hence show that the body descends a distance (g/2k^2)+(u/k)(1-ln2) before all the inflammable material is burnt.


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