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Units of many physical quantities on Earth are historically tied to the properties of our planet. What would be the units such as meter, knot or atmosphere, if we defined them using the same methodology as on Earth, but while living on Mars? Derive both the ratios between „terran“ and „martian“ units and their values in SI units.

Measure at least three physical properties of the smallest coin of legal tender in your country. We consider macroscopic dimensions as one property. We evaluate not only the accuracy of the measurement and the detail of the description but also the originality in the selection of quantities.

Think about the possibilities for simplification of movement of a human through a landscape during winter. Consider different terrain inclinations, types of snow („powder“, wet snow, melted and resolidified snow, ice, \dots ), and equipment (snowshoes, skis, crampons, ice skates, \dots ). Describe the physical principle behind each type of equipment, and based on this principle, determine which type is best suited for which environment.

Gnomes decided to forge another magic sword. They make it from a thin metal rod with radius $R=1 \mathrm{cm}$, one end of which they maintain at the temperature $T_1 = 400 \mathrm{\C }$. The rod is surrounded by a huge amount of air with the temperature $T_0 = 20 \mathrm{\C }$. The heat transfer coefficient of that mythical metal is $\alpha = 12 \mathrm{W\cdot m^{-2}\cdot K^{-1}}$ and the thermal conductivity coefficient is $\lambda = 50 \mathrm{W\cdot m^{-1}\cdot K^{-1}}$. The metal rod is very long. Where closest to the heated end can gnomes grab the rod with their bare hands if the temperature on the spot they touch is not to exceed $T_2 = 40 \mathrm{\C }$? Neglect the flow of air and heat radiation.

The two-second rule is a driving principle which states that a safe time distance between two vehicles is at least two seconds long. Suppose a traffic junction where a $n_1$-lane road changes into a $n_2$-lane one. The maximum allowed speed in the first section is $v_1$. What is the lowest possible maximum speed $v_2$ that can be allowed in the second section so that there is no traffic jam and everyone can follow the two-second rule? The average length of a car is $l$ and it can change its speed in leaps.

You may have noticed that not all volcanos on Earth have the same „universal“ shape – they differ from each other. For example, compare the photos of the Hawaiian volcano Mauna Loa and the Italian Vesuvio. They differ not only in the steepness of their walls but also in the style of eruptions. Both of these properties are related to the viscosity of magma. Discuss the effect of the viscosity of magma on the style and dangerousness of eruptions. Is is related to the geographic location of the volcanoes?

Take a glass, can or any other cylindrically symmetrical container. Measure the relationship between the angle of inclination of the container when it tips over and the amount of water inside of it. We recommend to use a container with greater ratio of its height to the diameter of its base.

Estimate how much the complete glaciation of an ice hockey rink costs.

We are sorry. This type of task is not translated to English.

Travel by airplane affects the atmosphere not only by well-known carbon emissions. Discuss how the aircraft industry affects warming of the atmosphere of Earth.