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a rocket of mass M is flying through a dust cloud the cloud has a density of P. the rocket's cross section is A. every dusticle the rocket colides with becomes permenantly attached.

the rocket is ejecting material (as a propellant) at the same rate that it assimilates it. the speed of the ejection relative to the rocket is

[tex]V_g [/tex]

find the rockets acceleration as a function of its speed V

2. Relevant equations

[tex]

F = M{{dv} \over {dt}} + (u - v){{dm} \over {dt}}

[/tex]

3. The attempt at a solution

i'v found dm, i think:

[tex]

dm = APdx = APVdt

[/tex]

so presumably, to find

the acceleration i did this:

[tex]

\eqalign

& dV = adt - V_0 = V_1 - V_0 \cr

[/tex]

[tex] & - V_0 dm = - V_g dm + MV_1 \cr[/tex]

but now im totally stuck...

any help? please?

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# Rocket accelerating thru a dust cloud

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