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(3 points)3. Series 37. Year - 1. it's too dry in here

Danka has a humidifier in her dorm room, which evaporates water from its boiling point to create warm steam. The device can hold a maximum of $V = 3,8 \mathrm{l}$ of water, which it uses up in $t = 24 \mathrm{h}$. What is its efficiency, i.e., what fraction of the energy drawn from the electrical grid it uses to convert the water to steam? The input power of the humidifier is $P = 260 \mathrm{W}$, and Danka put water at $T_0 = 20 \mathrm{\C }$ inside. All the necessary properties of water can be looked up.

(10 points)2. Series 37. Year - P. height of mountains

Which factors influence the height of mountains on different planets? Make an attempt at a quantitative estimate. You can consider the highest mountains on the Earth, Mars, and other known planets.

Karel was admiring Olympus Mons.

(10 points)1. Series 37. Year - P. rocket

Using current technology, how much fuel would it take to carry an object of mass $m=1 \mathrm{kg}$ into low Earth orbit?

(3 points)6. Series 36. Year - 1. canoeing mystery

In sunny summer weather, we observe interesting wind behavior on the river during the day. It is cold in the morning at sunrise, and sometimes there is even morning fog. The fog then quickly dissipates, and the air temperature rises. A light wind then blows up the river. In the evening, the situation calms down, and the wind direction turns downstream as the sun lowers toward the horizon. What causes this phenomenon? Explain the ongoing processes in these two cases.

Katarína was floating down the river and observing.

(7 points)6. Series 36. Year - 4. light faster than light

There is a laser in the distance $L$ from a large screen. Initially, the laser shines on the screen so that the distance from a laser spot on the screen to the laser is $R > L$. Then at the time $t=0 \mathrm{s}$, we begin to rotate the laser at a uniform angular speed $\omega $. Consequently, the distance of the spot on the screen from the laser decreases to $L$ and then increases back to $R$. What is the speed of this laser spot relative to the screen? Is it possible that the spot moves at a speed greater than the speed of light in a vacuum? Is there a limit, can it be infinite? How (qualitatively) does this speed depend on the spot's position on the screen? The whole apparatus is in a vacuum.

Marek J. wanted to verify statements about the apparent surpassing of the speed of light.

(10 points)3. Series 36. Year - 5. guitar

Assume you have a guitar that is perfectly tuned at room temperature. By how many semitones (in tempered tuning) will the individual strings be out of tune if we move to a campfire, where it is cooler by $10 \mathrm{\C }$? Will the guitar still sound in tune? The distance between the string attachment points is $d = 65 \mathrm{cm}$. The strings have a density $\rho = 8~900 \mathrm{kg.m^{-3}}$, a Young's modulus of elasticity $E = 210 \mathrm{GPa}$ and a thermal expansion coefficient $\alpha = 17 \cdot 10^{-6} \mathrm{K^{-1}}$.

Honza's guitar is out of tune again.

(9 points)3. Series 36. Year - P. absurd pendulum

What phenomena can affect the measurement of gravitational acceleration using a pendulum? Estimate how many valid digits your result would have to contain to measure them. Consider also the phenomena that you usually neglect.

Kačka was wondering what she could write in the discussion.

(12 points)2. Series 36. Year - E. the loudspeaker

Measure the dependence of sound intensity emitted by your loudspeaker/mobile phone/computer on the distance from the source. Furthermore, determine the dependence of sound intensity on the settings of the output volume. Do not forget to fit the data.

Jarda cannot hear much in the back row.

(12 points)6. Series 35. Year - E. minute

Create a device that can measure one minute as accurately as possible. You are not allowed to use any time measuring devices for calibration when designing your own. After you finalize your device, use a stopwatch to determine „your minute“ accuracy.

Bonus: Measure ten minutes.

Matěj allways arrives at the train station at most one minute before the train's departure, even if it's got a half hour delay.

(10 points)6. Series 35. Year - P. torrential rain

Is it convenient to hide from the rain in the woods? Create a suitable model describing this issue. Consider, for example, foliage density, and the intensity and duration of the rain. Describe how long after the rain starts, the drops from the leaves start to fall to the ground, as well as how long after the rain ends, it stops raining in the woods, and so on.

Lucka ran through the woods and got completely wet.

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