Bug Brainteaser

[Beaker]

Seeing as the last brainteaser was a good topic of discussion. I have found another one for us all! :D

A bug walks down a rubber band which is attached to a wall at one end
and a car moving away from the wall at the other end. The car is moving
at 1 m/sec while the bug is only moving at 1 cm/sec. Assuming the
rubber band is uniformly and infinitely elastic, will the bug ever
reach the car?

Skatie

[Jolly_MG_Maestro]

No it won't, if the elasticity of the band is infinite, and assuming the bug stays on it indefinitely and doesn't move, the bug will still be travelling at a slower rate of speed than the car and so will never catch it up, only increase the distance between bug and car.

[Dave]

The bug will never catch up.

Dave

[Jonathan]

The bug will be torn in half.

[Mat_C]

Bug will catch the car - it'll take him a while. The elastic the bug is standing on is moving as well!

[Dave]

The bug will catch up... i know, i changed my mind after I thought it through:

Speed of bug=1
Speed of Car=100
Car Speed divided by bug speed = 100

make 101 (imaginary) equally spaced lines on the rubber band. When the bug is at line1, line2 is moving away at 1/101 * 100m/s ie he will catch up to that one because 1/101*100 is less than 1cm/s (the line is moving away from him slower than 1cm/s
Then the next line, then the next...
Now when he gets to the second to last stripe, the instant he stands on this stripe he is traveling exactly the same speed as it, then beyond this strip he is traveling faster the stripe so once he crosses that line he is gaining on the car.

So he does get there!!

Dave.

[Beaker]

I have a feeling you got a First in Mathematics at degree didn't you Dave?

That is a perfectly correct and feasible answer

Skatie

[Wonko_The_Sane]

The other question is, when the bug hits the car..how hard will it be to get the wipers to clear the screen of it's remains without making a smeary mess?

[SimonR]

Is there a way of working out how long it'd take for the bug to reach the car now we've established that it can?

If you can work that out then you'll know how far the car (and bug) travelled, but more importantly, (assuming that each bug stride is about 1mm) how many steps it had to take.

You can then also work out how much fuel the car used, assuming that it was a Mk.1 Maestro with digital dash and working ECU, which is probably about as likely as an infinately stretching elastic band!

[Dave]

Im sure all these things could be worked out if I had the time or the desire.

I think the best bet is we take an infinite elastic band, and well trained bug, and a Mk1 Maestro with working digi dash/comp to the XMas dinner... then using a stopwatch we can test the theory out in the car park.

Dave

[Beaker]

lol :laugh: Yes we can test it along with the balloon :laugh:

Here was the official solution to the question anyway.

Let w = speed of bug and N = ratio of car speed/bug speed = 100. Paint
N+1 equally spaced stripes on the rubberband. When the bug is standing
on one stripe, the next stripe is moving away from him at a speed
slightly < w (relative to him). Since he is walking at w, clearly the
bug can reach the next stripe. But once he reaches that stripe, the
next one is only receeding at < w. So he walks on down to the car, one
stripe at a time.

The bug starts gaining on the car when he is at the next to last
stripe.



Skatie

[G Force]

Lets all hope the wall don't give way or the last thing to go through the bugs mind will be its b@lls!!!

Sorry the old ones are sometimes not the best I know.... Gary :laugh: