20090331, 11:06  #1 
Oct 2004
Austria
9B2_{16} Posts 
How fast is the dog?
A dog decides to run 500 km. It has got an empty cane tied on its tail, which hits the ground exactly once every second with a loud "clonk!" sound.
The dog starts its run with the first clonk it hears, with a velocity of 2 m/s. Afterwards it doubles its velocity instantly (i.e. with infinite acceleration) every time when it hears a clonk from the cane. How fast is the dog when it reaches its destination? 
20090331, 11:16  #2 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Assuming Newtonian mechanics, 262144m/s.
Alex Last fiddled with by akruppa on 20090331 at 12:28 Reason: I'm seriously not getting this puzzle, then :( 
20090331, 11:24  #3 
Oct 2004
Austria
2482_{10} Posts 

20090331, 12:04  #4 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Are you sure? I get the same answer. I made a script for my calculator to find it by summing, but here's a more advanced way to describe the logic:
At x seconds, (where x is an integer) the dog was running at 2^x m/s, accelerates to 2^(x+1) m/s, and has traveled 2^(x+1)2 m (2^(x+1)2 is equivalent to the sum of 2^1 ... 2^x and I might've used that instead, but 1. TeXformatted equations, like I'd need to use the Sigma function, don't spoilerize, and 2. I don't already know the TeX format for Sigma). 2^(x+1)2 first becomes 500000 or higher during the 18th second, and 2^18=262144, so the dog was running at 262,144 m/s when he passed the 500 km mark. On a side note, I think it took the dog approx. 17.907 seconds to reach the 500 km mark. Last fiddled with by MiniGeek on 20090331 at 12:24 
20090331, 12:06  #5 
Nov 2006
Singapore
3·5^{2} Posts 
Umm... 0 m/s.If it has reached its destination it would have stopped...:smile:

20090331, 12:16  #6 
Nov 2006
Singapore
3×5^{2} Posts 
Otherwise I have to agree with akruppa and MiniGeek

20090331, 12:31  #7 
"William"
May 2003
New Haven
2×3^{2}×131 Posts 
512 m/s. This is the doubling that passes the speed of sound for reasonable temperatures. After that point, the dog never hears another bounce of the cane. [url]http://hyperphysics.phyastr.gsu.edu/hbase/sound/souspe.html[/url] 
20090331, 12:35  #8 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Clever. I thought there must be some trick to it...
Alex Last fiddled with by akruppa on 20090331 at 12:36 Reason: Duh. Doppler effect misunderstanding removed. 
20090331, 12:51  #9 
Oct 2004
Austria
2×17×73 Posts 
@wblipp  correct!

20090331, 12:56  #10 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4267_{10} Posts 
I thought it was odd that the question was phrased that way, (about hearing the clonk instead of just that every second he doubled his speed) but you never specified the speed of sound in the atmosphere the dog is running, so how were we to know that this dog that can accelerate instantly and run 500 km at once happened to be in our atmosphere under standard conditions, and not in some hypothetical medium that transfers sound faster than 262144 m/s?

20090331, 13:06  #11  
Oct 2004
Austria
2×17×73 Posts 
Quote:


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