- #1

devious_

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A body consists of equal masses [itex]M[/itex] of inflammable and non-inflammable material. The body descends freely under gravity from rest. The combustible part burns at a constant rate of [itex]kM[/itex] per second, where [itex]k[/itex] is a constant. The burning material is ejected vertically upwards with constant speed [itex]u[/itex] relative to the body, and air resistnace may be neglected. Show, using momentum considerations, that

[tex]\frac{d}{dt}[(2-kt)v] = k(u-v) + g(2-kt)[/tex]

where [itex]v[/itex] is the speed of the body at time [itex]t[/itex]. Hence show that the body descends a distance

[tex]\frac{g}{2k^2} + \frac{u}{k} (1 - \ln 2)[/tex]

before all the inflammable material is burnt.

I managed to do the first part, but I have no idea how to approach the second.