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Imagine a ferry in the shape of a rectangular cuboid with a weight $M$, length $L$, width $W$, and height $H \ll L$ from the keel to the deck. After docking at the pier, passengers gradually exit through the back of the deck so that the empty front part of the deck becomes larger and the area density of people on the filled part does not change in a different way. Find the maximum weight of passengers the ferry can carry so that no part of the deck is below the surface when people disembark. Consider that the ship is stable in the transverse direction and that people get off slowly.

Build an apparatus that can measure the smallest possible ripples on the surface of the liquid. You can choose the container yourself – it can be a cup, a bottle, or something else. Thoroughly describe and take a picture of the whole apparatus. Determine the minimum amplitude you are able to measure.

Discuss what physical phenomena affect the cruising speed of a ship and submarine. What resistive forces act on them? What is the highest cruising speed that a ship or submarine can sail?

Danka attached a garden hose with an inner diameter of $1{,}5 \mathrm{cm}$ to a tap in her dorm room and placed the other end on the edge of a window on the eighth floor, $23 \mathrm{m}$ above the ground. What is the necessary volumetric flow rate of the water tap so that Danka can spray a stream of water on the people disturbing the night's silence? They are standing below the window at a horizontal distance $9 \mathrm{m}$ from the building. Is Danka able to achieve this if water is being sprayed horizontally from the hose and there is no wind?

Bonus: Where is the farthest these people can stand so Danka can still spray them if the volumetric flow rate of the tap is $0{,}4 \mathrm{l\cdot s^{-1}}$? Danka can now set the end of the hose so that water sprays at an arbitrary angle to the horizontal plane.

Water flows through a water channel of rectangular cross-section, and width $d=10 \mathrm{cm}$. A leaf falls on its surface and starts moving with a velocity of $60 \mathrm{cm\cdot s^{-1}}$. The height of the water in the channel is $h=1{,}3 \mathrm{cm}$. Estimate how long it will take to fill up a $50 \mathrm{l}$ bucket. Comment on the assumptions used in comparison with the real situation.

Let us have an ideal scale which we calibrate using a state standard (etalon) with a mass $m\_e = 1,000~000~165 kg$ and a density $\rho \_e = 21~535,40 kg.m^{-3}$. By calibration, we mean that after placing the standard on the scale, we assign to the measured value the mass $m\_e$. The unknown object is weighed under the same conditions in which its volume is $V_0 = 3,242~27 dl$. What mass did we measure if we measured the weight $G = 1,420~12 N$? What is the actual mass of the object? The experiment is conducted at a place with standard gravitational acceleration $g = 9,806~65 m.s^{-2}$ and air density $\rho \_v=1,292~23 kg.m^{-3}$. Take into account that the calibration is linear, and the unloaded scale shows zero.

Measure the density of ice.

Estimate the consumption of electrical energy for one trip of the IC Opavan train. The train set consists of seven passenger cars, a 151-series locomotive and is capable of reaching a speed of $v\_{max} = 160 \mathrm{km\cdot h^{-1}}$. For simplicity, consider that all passengers are going from Prague to Opava.

A cylindrical capsule (Puddle Jumper) with a diameter $d = 4 \mathrm{m}$, a length $l = 10 \mathrm{m}$ and with a watertight partition in the middle of its length is submerged below the ocean surface and falls to the seabed at a speed of $v = 20 \mathrm{ft\cdot min^{-1}}$. At the depth $h = 1~200 ft$, the glass on the front base breaks and the corresponding half of the capsule is filled with water. At what speed will it fall now? How long will it take for the capsule to sink to the bottom at the depth $H=3~000 ft$? Assume that the walls of the capsule are very thin against its dimensions.

There are several movie scenes where a car falls into water together with its passengers. Calculate the torque with which a person must push the door in order to open it at the bottom of a lake if the bottom of the door's frame is $8,0 \mathrm{m}$ deep underwater. Assume that the door is rectangular with dimensions $132 \mathrm{cm} \times 87 \mathrm{cm}$ and opens along the vertical axis.