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### (5 points)2. Series 28. Year - P. problem of the travelling salesman

When digital mobile phones started to be more common there was often an issue with accepting calls in a car. Nowadays this issue is mostly connected with trains. What factors influence the transmission of data in the GSM network and how can they influence the availability of the signal of the provider? How can one combat this problem?

Ales P. was travelling first class by train and he thought something up.

### (2 points)4. Series 27. Year - 1. Another unsharpened one

A freshly sharpened pencil 6B has a tip in the shape of a cone and the radius of the cone's base is $r=1\;\mathrm{mm}$ a and its height is $h=5\;\mathrm{mm}$. How long will the line that we are able to make with it be if the distance of two graphite layers is $d=3,4Å$ and the track of the pencil has on average $n=100$ such layers?

Mirek was calculating how long his pencils will last.

### (5 points)4. Series 27. Year - P. the true gravitational acceleration

Faleš wanted to determine the gravitational acceleration from an experiment in Prague(V Holešovickách 2 in the first floor/ground floor). In the experiment he was dropping a round ball from a height of a couple of meters above the Earth. Think about what kind of corrections he had to apply when analysing the data. Then think up your own experiment to determine g and discuss its accuracy.

Karel was thinking about the difference between gravitational acceleration and gravitational force

### (5 points)3. Series 27. Year - P. solar power

Can a plane fly using a solar power?

Dominika with Honza and Michal wanted to fly away to warmer countries.

### (2 points)1. Series 27. Year - 1. golden dam

How many bricks of 24-karat gold can you fit into the Orlík dam? What would be the pressure acting on a brick placed at the deepest point? The dimensions of a brick are 10 cm, 3 cm a 1 cm.

Karel wants to be rich.

### (4 points)5. Series 26. Year - P. Prague is flooded!

In 2002 Prague experienced serious floodings. Try to estimate the amount of water that can fit into the Prague subway system. All the important parameters of the subway system like the train sizes, number of stations, length of the tunnels etc. can be found online.

Karel was drowning.

### (2 points)4. Series 26. Year - 1. Who cares about Einstein?

Who is your favorite physicist except of Albert Einstein? What were her contributions to physics? Why do you consider her to be so brilliant? Why should she be famous? Write a short essay about her life and the discoveries she made.

Karel loves history.

### (5 points)3. Series 26. Year - P. Conspiracy theory?

In this problem you are asked to think about the vapor trails that sometimes form behind an airplane. What are the physical parameters that determine the length of these lines? Estimate and/or find the values of these parameters and determine the range of all possible lengths. Use your results to dismiss the myth of chemtrails that says that these lines are formed by poisonous chemicals being released from the planes.

Michael declared a war on stupidity.

### (8 points)2. Series 26. Year - E. it's fall again

Estimate the average surface area of a leaf of your choice. We are looking forward to see a thorough statistical analysis of your measurements! Use your result to estimate the fraction of energy obtained from the Sun that is used to make saccharides.

### (2 points)1. Series 26. Year - 1. paper

Try to find out dimensions, mass and density of a regular A4 paper (one that you would use in a printer). Given these values estimate its average thickness.

Karel was eating a piece of paper.