Topic: The super-dog
 Message: Posted by: Nir Dahan (Mar 5, 2006 04:07PM)
I don't know if I ever told you about the super-dog incident.
superdog can run extremely fast and increase his speed in an instant.
one day we were hiking along a very long straight rail tracks. I tied a rusty can to super-dog's tail.
we started at a nice pace of 1 meter per second.
as we ran the rusty can hit the tracks and made a sound that drove super-dog nuts. each time he heard the "cling" sound he would double his speed in an instant.
naturally I couldn't keep up with him.
can you tell how fast did super-dog ran at the end of the day? or how many times did superdog increased his speed?
 Message: Posted by: magicjohn2278 (Mar 5, 2006 05:53PM)
No, I can't, because it all depends on the air temperature, which you haven't told me.

If you said that the air temperature was 30 degrees centigrade, then I would deduce that superdog's final speed at the end of the day would be in the region of 349.7m/s.
 Message: Posted by: Nir Dahan (Mar 5, 2006 05:54PM)
Given the air temperature you stated you would still be wrong,
sorry you miss out on a few things
 Message: Posted by: magicjohn2278 (Mar 6, 2006 05:54AM)
293199.7 mph?
 Message: Posted by: mike paris (Mar 6, 2006 07:37AM)
I don't think at that speed the tin would hit the ground and so not bang on the tracks,so I think the dog would run until exhausted and stop DEAD.
 Message: Posted by: Nir Dahan (Mar 6, 2006 08:52AM)
Tomas suggested eliminating the tracks and assuming the dog runs on a smooth road.
I accept this correction, and the problem is changed from now on.
this helps avoiding an ambiguity in the problem.

thank you Tomas

Nir
 Message: Posted by: 0pus (Mar 6, 2006 11:00AM)
512 m/s.

Doubled speed 10 times.

0pus
 Message: Posted by: Nir Dahan (Mar 6, 2006 02:42PM)
You missed something opus he will go much faster than this
 Message: Posted by: 0pus (Mar 6, 2006 10:02PM)
Let me try again.

131,072 m/s.

Doubled speed 17 times.

0pus
 Message: Posted by: Steve Martin (Mar 7, 2006 07:54AM)
We are not told how frequently the can bangs on the road, or how long there is until "the end of the day".

Therefore, assuming that there is enough time left in the day, and that the can bangs pretty continuously (as one would imagine it would if tied with a length of string to the dog's tail) the dog's speed will double every few seconds.

After 1 bang, his speed is 2 m/s
After 2 bangs his speed if 4 m/s
After n bangs his speed is (2 ^ n) m/s

After 29 bangs the dog would be travelling at 536,870,912 m/s - faster than the speed of light (which is 299,792,458 m/s) but that would be IMPOSSIBLE (according to Einstein's theory of relativity which states that nothing can travel faster than the speed of light).

Therefore, the maximum speed of the dog would be reached on the 28th bang of the can. At that point, the speed of the dog would be (2 ^ 28) = 268,435,456 m/s

It may be, of course, that on the 29th bang, the dog tries to double its speed and, finding that it can't, settles for the speed of light instead. Either way, you would have to put up some "lost pet" notices, as by then super-dog would be many millions of kilometres from home.
 Message: Posted by: magicjohn2278 (Mar 7, 2006 06:17PM)
[quote]
On 2006-03-06 23:02, 0pus wrote:
131,072 m/s.
[/quote]

... or about 293199.7 mph? (See my previous post!)
 Message: Posted by: landmark (Mar 7, 2006 06:32PM)
At a certain point the dog is going faster than the speed of sound; now things start to get quiet.

Jack Shalom
 Message: Posted by: Daegs (Mar 8, 2006 02:34AM)
He would be going zero at the end of the day, the jolt of increasing his speed so suddenly would be like a sledgehammer hitting his whole body and it would kill him.

Assuming he is Invincible to that, and assuming the can hits every walk cycle, then at the end of the day he would be going 2^n where where (2^(n-1) < the speed that will keep the can afloat due to air resistance and 2^n > that speed).

I think he would hit that before the speed of sound....

But if going with speed of sound, the dog would be going 512m/s(speed of sound at sea level being 340m/s)

However.... I still say that air resistance would stop the can from banging before he reaches sound, say about 64m/s.... that's about 143MPH and would be sufficent imho to keep it afloat....

I would say it depends on his tail and how rigid it is, where the string is tied and how long the string is and the shape/size of the can.
 Message: Posted by: magicjohn2278 (Mar 8, 2006 03:40AM)
[quote]
On 2006-03-08 03:34, Daegs wrote:
Assuming he is Invincible....
[/quote]

I think you have to assume that superdog (was it Krypto or am I just making that up?), has most of Superman's powers, super-speed, x-ray vision, super-breath, super-hearing, heat-vision, super-strength, etc. etc!
 Message: Posted by: Nir Dahan (Mar 8, 2006 09:03AM)
[quote]
On 2006-03-07 08:54, Steve Martin wrote:
We are not told how frequently the can bangs on the road, or how long there is until "the end of the day".

Therefore, assuming that there is enough time left in the day, and that the can bangs pretty continuously (as one would imagine it would if tied with a length of string to the dog's tail) the dog's speed will double every few seconds.

After 1 bang, his speed is 2 m/s
After 2 bangs his speed if 4 m/s
After n bangs his speed is (2 ^ n) m/s

After 29 bangs the dog would be travelling at 536,870,912 m/s - faster than the speed of light (which is 299,792,458 m/s) but that would be IMPOSSIBLE (according to Einstein's theory of relativity which states that nothing can travel faster than the speed of light).

Therefore, the maximum speed of the dog would be reached on the 28th bang of the can. At that point, the speed of the dog would be (2 ^ 28) = 268,435,456 m/s

It may be, of course, that on the 29th bang, the dog tries to double its speed and, finding that it can't, settles for the speed of light instead. Either way, you would have to put up some "lost pet" notices, as by then super-dog would be many millions of kilometres from home.
[/quote]

mmm no!

look at opus answer. maybe he can explain how he got to the solution.

nir
 Message: Posted by: Steve Martin (Mar 8, 2006 09:10AM)
OK, so it has something to do with the speed of sound, because the dog hears the bang.
 Message: Posted by: Andrei (Mar 29, 2006 11:16AM)
Nir - how physics-friendly is the problem?

As in, does the dog create an aerodynamic tunnel of air behind him? If so, he will pretty much always hear the can bouncing up and down.

Andrei
 Message: Posted by: Jonathan Townsend (Mar 29, 2006 02:55PM)
If the sound of the can hitting the ground is the trigger to double its speed.
Then when it gets to the speed of sound we have a halt condition.
However, that presumes the can will be hitting the ground even at high speeds.
Let's consider the terminal velocity of a can... likely about 100/200mph tops.
At that speed, the thing will be pretty much flying and no longer hitting the ground, so let's put 256 at my guess on the high end there, else 1024 as just over the speed of sound in MPH.
 Message: Posted by: Andrei (Mar 29, 2006 03:07PM)
Jonathan, the dog and the can are at relative speed 0 to one another. If the air between them is trapped, due to some sort of aerodynamic effect, than, although the dog and can are travelling at a speed greater than that of sound, the dog will still hear the can bouncing off the ground.

It's like the whole "If you're in an aeroplane travelling at the speed of sound, and you make a noise, what will happen?" thing.

Andrei
 Message: Posted by: Jonathan Townsend (Mar 30, 2006 09:31AM)
How much tension can the string take?
just occured that an instantaneous acceleration (impulse) would snap the string. :)
 Message: Posted by: Andrei (Mar 30, 2006 09:36AM)
True.

Andrei