(adsbygoogle = window.adsbygoogle || []).push({}); A mouse is sitting at one end of an infinitely-stretchable rubber sheet that is initially one kilometer long. One end is nailed to a wall, and the other end is tied to a Japanese bullet train. The mouse begins to walk forward at a constant speed of 10 centimeters/second. At the same time the train begins to move forward at the constant speed of 100 meters/second, stretching the rubber sheet.

Question 1: Will the mouse ever reach the end?
Question 2: If so, how long will it take?

Showing all work and logic, the first person to correctly answer Q1 will receive 50,000 vBux. The first person to correctly answer Q2 will receive 250,000 vBux. The same person can, but does not have to, answer both questions.

That would certainly be too easy :p. Give it a little more thought.



The mass of the train and the band's elasticity are irrelevant. All you need to know is that the band doesn't break.

Distance 100 x 1000 = 100,000 cm

10*60= 600 Mouse speed per min
600/ 100,000 = 166.666666667 how long it would take the mouse over 1 kilometer.

160.666 mins
Which I think due to changing it back to meters makes it 16mins.

Train

1000 metres

100*60 = 6000

1000/6000 = 0.166 secs

Now my brain has stopped working.

*Could be wrong.

The answer is 5

Hint: what effect does the expanding rubber sheet have on the motion of the mouse?

Since the rubber sheet is going to begin stretching, it is going to be increasing in length but the mouse is still in place on it. As it stretches, he will be moving with the sheet, and his speed of 10cm/s will be added on to that. He would probably reach the train fairly quickly, but I'm far too tired right now to try and determine how fast.

That's on the right track. If you could make it a little more precise then the 50k is yours.

Q1: If the train is moving at 100 meters a second, then so is the rubber sheet. But the mouse is on the rubber sheet so it means its moving at 100 meters a second aswell and plus the 10cm the mouse is walking. So the mouse will reach the end.

Q2: It will take 1 second.

Mouse:

10 cm/s

Train:

100 m/s

Band stretching which adds on 100 m/s to mouses speed

For every 100 meters the train travels, the mouse travels 100.1 meters(?) because 10 centimeters per second is equivilent to 0.1 meters per second.. so plus the trains speed and the speed of the mouse, he moves 100.1 meters per second every second.

Dependant on how long the sheet was before it was stretched would help but..

The mouse would reach the end in under an hour!

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Scrap that
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10 Cm/s is equivelant to 0.1 m/s
100 m/s is equivelant to 10,000 cm/s

So im guessing something to do with that but this is hard

You had the right idea, but the above isn't correct. If the mouse is standing on the end of the band next to the train, then the additional speed it picks up will be 100 m/s. But what about when he's near the beginning? The other end is nailed to a wall, which doesn't move at all, so the additional speed the mouse picks up is zero.