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# Motion with variable mass help Watch

1. Need help with this M5 question. I have got dm/dt = -kM0, so m = M0(1-kt) hence t = 1/(10k). I also have g(M0 - m) = m(dv/dt). Any help would be appreciated! Just struggling piecing it together

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2. (Original post by Jooooshy)
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Sub your value for m into your F=ma equation, and this will give you something to work with.
3. But now I am left with M0ktg = (M0-M0kt)(dv/dt).. To integrate this I would need to use by parts? Really struggling.. Is what I have currently got correct?

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4. (Original post by Jooooshy)
But now I am left with M0ktg = (M0-M0kt)(dv/dt).. To integrate this I would need to use by parts? Really struggling.. Is what I have currently got correct?
Looks fine.

M0 cancels. Rearrange prior to integration. Then clean up the improper fraction. You won't need IBP.
5. Thank you so much. Out of curiosity, how did you clean up the improper fraction? I used a substitution to do it.. Is there an easier way? Thanks again it is really appreciated!

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6. (Original post by Jooooshy)
Thank you so much. Out of curiosity, how did you clean up the improper fraction? I used a substitution to do it.. Is there an easier way? Thanks again it is really appreciated!

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Polynomial division would do it.

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