- #1
Gregie666
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hi...
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
[tex]
F = M{{dv} \over {dt}} + (u - v){{dm} \over {dt}}
[/tex]
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 I am totally stuck...
any help? please?
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
Homework Equations
[tex]
F = M{{dv} \over {dt}} + (u - v){{dm} \over {dt}}
[/tex]
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 I am totally stuck...
any help? please?
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