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### 6. Series 24. Year - 3. airplane

How long does it take before the Sun rises and sets as seen from an air-plane that flies in the ecliptic plane? In the same situation how long is a day? What about night? Necessary information like typical height at which air-planes fly can be surely found on the Internet. Answer these questions for an air-plane flying both east and west.

### 6. Series 24. Year - E. the discworld

Think of as many ways to verify that the Earth is spherical as you can. If you do verify this statement find a way to measure the radius of the Earth.

### 6. Series 24. Year - P. the water porter

How much water can be taken out of a swimming pool (in one trial) using only your hair (assume you have a lot of them)?

### 4. Series 24. Year - E. Depressed egg

Determine the maximum height a typical egg can fall from without breaking itself. How does the result change if you wrap the egg in some protective material which is not thicker than 5$\;\mathrm{mm}?$ Try couple of different materials.

Karel

### 3. Series 24. Year - 1. Warm-Up

*Dr. Nec.*

There are two ways to measure the amount of wood in a pile of trees. Either as the volume of pure wood in the pile or as the volume of wood together with the empty spaces in the pile. Find the conversion factor between these two units assuming the trees are cylinders of radius $r$ that are layed one on top of the others.

*Bubbles.*

A spherical cap of radius $r$ is made by blowing air into a circular surface of soap water. Estimate the velocity of air molecules hitting the surface?

Jakub

### 2. Series 24. Year - 1. Warm-Up

*Jakub's breakfast*

Every morning Jakub enjoys his favourite cereals which he pours into a bowl of milk. Assume the bowl is of circulur frustum shape with upper and lower radius $R$ and $r$ respectively ($R$ \geq r$)$, that the cereals are little solid spheres and that before he puts the cereals into the bowl there is milk of height $h$. What is the maximum amount of cereals he can fit into the bowl? You also know that the fraction of volume the cereals occupy inside a fully filled box is $\kappa$.

*Magnetic monopole*

Let's have a metal plate magnetized in such a way that the upper and lower sides are the north and south poles respectively. We use these plates to create two semispheres with the outer side being the north pole. Now, if we glue these two semispheres together, we effectively get a magnetic monopole, which, as we know, can not exist in our world. Where did we go wrong?

eee

### 6. Series 23. Year - 2. John the voyeur

John is standing on the top of the Žižkov Tower and looks into the windows of neighbouring houses. All the windows face the tower, are of same size and are at the same height. Calculate the radius of the lowest privacy in the houses with such windows. John does not have any binoculars.

### 2. Series 23. Year - 1. calamity

One of organizers of Fykos was travelling by train back home. The train was locked in by a snow storm. He was bravely counting snow flakes behind the window and was thinking: „How many snow flakes are in 1kg of snow?“ Are you able to make qualified guess to this question?

vzpomínáme na neznámého padlého

### 2. Series 23. Year - E. metronome

If you play any musical instrument, then sometimes you experience problems with rhythm. Define an experiment and measure which frequency (knocking onto a table, pushing piano keys etc.) is easiest to keep. Is there any correlation between other natural effects?

Parkinsonem onemocněl Honza Hermann

### 1. Series 23. Year - 1. text scrolling in underground

Information system in Prague underground has following feature: during scrolling text on the display to the left, the letters are *tilted*. Is there a simple way how to do this function on „hardware“ level? What effect will have this at text scrolling in vertical direction?
Assume, that information display consists from LEDs spaced in orthogonal grid.

Ze tmy tunelu přitáhl Byrot.