potpourri iv

[Ghost Post]

Somebody please explain #3. How could the ant ever reach the other end?

[Gomez]

I think that when the rubber band stretches by 1 meter, the ant is carried along with it so for every meter the rubber band travelled the ant travelled 1 meter & 1 centimeter, I think.

[Ghost Post]

The rubber band stretches evenly, so when the ant is on the rubber band some of the stretch is ahead of the ant and some of the stretch is behind the ant. So if the rubber band stretches by a metre, the ant moves forward, but by less than a metre (I'm ignoring the ant's walking along the rubber band for now).

For example, if the ant is 10% of the way along the rubber band and the band stretches a metre, 10% of the stretch is between him and the anchor. So the ant moves away from the anchor by 10% of a metre (that's .1m).

On top of that, the ant walks 1 cm along the rubber band (that's .01m), so it moves a total of .11 m.

In general, if the rubber band is L metres long and the ant is x metres from the anchor, a 1 metre per second rubber band stretch moves the ant the fraction x/L of a metre per second. It's also walking at 0.01 metres for second.

So all together...

speed of ant = x/L + .01 metres per second

Knowing that, and thanks to a bit of calculus, you can figure out that the ant's acceleration is .01 metres per second, per second. I'm not gonna explain that, but there's gotta be introductory calculus in your local library.

Anyhoo, the ant is accelerating so eventually it's gonna be going faster than 1 meter per second (the speed that the end of the rubber band is moving) and is gonna catch up to the end of the rubber band.

So the answer is Yes, it will get to the end of the rubber band.