[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 489

[TheXpert]

Mischek:
Two cylindrical towers have the same height - 10 metres, the diameter of the first is 5 metres, the second is 2.5 metres. Around each tower there is a spiral staircase. The angle of the stairs to the horizon is constant everywhere and the same for both towers. A hobbit stands at the foot of each tower.

Question: Which of the hobbits will reach the top of the tower faster if they walk at the same speed?

The request is the same -- don't rush to peck at the answer.

[Alexey Subbotin]

and that it's hobbits is a prerequisite?

[TheXpert]

alsu:
and the fact that they are hobbits is essential?

Of course it is. They have hairy feet, so the chances of slipping are high :)

[ilunga]

TheXpert:
Sure. They have hairy feet, so the chance of slipping is high :)

And they will always slip at the same time :)

[Sceptic Philozoff]

The hobbits are probably provided for in case the diameter of the thin tower is very small - well, say, 20 centimetres.

[PapaYozh]

TheXpert:
Question: Which hobbit will get to the top of the tower faster, assuming they walk at the same speed?

There is one important clarification required. Which speed do you mean, angular or linear?

[TheXpert]

Don't mess around :)

[PapaYozh]

Mathemat:
The hobbits are probably provided for in case the diameter of the thin tower is very small - well, say, 20 centimetres.

Well, it says everything about the towers, but not about the width of the stairs. By the way, this problem, unlike the previous one, has inaccurate conditions. The point is that the angle of inclination to the horizon on the outside of the stairs is always smaller than the angle of inclination on the inside. And this difference depends on the outer and inner radii.

[PapaYozh]

TheXpert:
Stop messing around :)

:)

It was more interesting about the maps.

[Andrey Dik]

We have to assume that the width of the ladder is equal to 0, i.e. they are just lines drawn on the sides of the cylinders.

From the first glance at the problem: the length of the line is shorter at the smaller diameter of the cylinder. This means that the hobbit will reach the top faster.