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Relativistic rocket equation question thingy
#1
Relativistic rocket equation question thingy
I found this question challenging and enjoyable;
[Image: 17f9.jpg]
[Image: pm49.jpg]

It's from a scholarship calculus exam I sat.
Post your solutions/attempts! Mine was rather long winded, I hope someone finds a more elegant method.
I have more pictures zoomed in if you can't see these properly.
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#2
RE: Relativistic rocket equation question thingy
This looks challenging... maybe I'll look into it when I get home, some 6 hours from now... Wink
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#3
RE: Relativistic rocket equation question thingy
Big Grin I thought this was going to be one of those threads that just dies.
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#4
RE: Relativistic rocket equation question thingy
What am I solving for?
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#5
RE: Relativistic rocket equation question thingy
Basically you're solving for (delta v).
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#6
RE: Relativistic rocket equation question thingy
Deceptively simple...
[Image: C360_2013-12-03-22-05-17-227_zps7525f143.jpg]

If there's anything you can't understand, I can take a better photo...

edit: bear in mind that ln = log_e
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#7
RE: Relativistic rocket equation question thingy
You can do it in a few lines if you solve for delta v, then just use the identity a^b = e^(ln(a^b)) = e^(b*ln(a))

b = 2u/c and a = m0/m1

All these types of problems can generally be solved with the identities ln(a*b) = ln(a) + ln(b) and ln(a^b) = b*ln(a)
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#8
RE: Relativistic rocket equation question thingy
(December 3, 2013 at 6:10 pm)pocaracas Wrote: Deceptively simple...



If there's anything you can't understand, I can take a better photo...

edit: bear in mind that ln = log_e

Nice job! you did it slightly different than I did, but we still used roughly the same process.

(December 3, 2013 at 7:03 pm)FreeTony Wrote: You can do it in a few lines if you solve for delta v, then just use the identity a^b = e^(ln(a^b)) = e^(b*ln(a))

b = 2u/c and a = m0/m1

All these types of problems can generally be solved with the identities ln(a*b) = ln(a) + ln(b) and ln(a^b) = b*ln(a)

What you're describing here seems to be roughly the same as what I did, and it takes more than "a few lines". If you mean something other than I understand, please post a picture of your solution.
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#9
RE: Relativistic rocket equation question thingy
Here's my solution. I skipped a few lines here and there, I can explain those if its not obvious.



Also, here is the second part of the question!

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