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The ladder is only 2 km long going to the platform, from which you have to take a stairs, which goes with long arch above the countryside. The staircase has very special shape: for each step you need the same amount of mechanical work. Calculate, how the step height depends on the distance from the Rama axis, if the length of stairs is constant. What shape is the arch?

Finally you got onto the surface of Rama. Suddenly it started to shake and you think the rotation speed has changed. How you can measure the rotation speed? Can you find more than one experiment?

Find the change in rotation speed of the Earth, if English and Scots would start to drive on right instead on left. Make just an estimation.

Find the properties of material, which you need to make a rope for a lift from geostationary orbit to the Earth surface. Is such material available on Earth?

A small ball is thrown in horizontal direction onto a inclined plane. The ball starts to jump on the plane and after $Ncontacts$ it falls at right angle onto the plane. An example of such trajectory for $N=4$ is in figure. What is the inclination angle of the plane $α?$ Assume, the ball bounce elastically, do not assume rotation.

You travel in fast train and are looking outside of the open window. Three windows in front of you someone spits a chewing-gum. How long do you have to get back to coupe to avoid contact with chewing-gum? The chewing-gum is spherical shape and was not thrown out, but just laid in air flow.

Calculate a slope of front glass of a car, so that water drops at speed 80 km ⁄ h do not run off, but to the sides. Verify that you results is compatible with reality. What else influence the slope of front window?

Investigate following phenomenon: while in a moving train looking out of window, the objects at horizons do not move too fast. But objects close to window (e.g. telegraph poles) move extremely fast behind the window. How is this apparent speed related to the distance from the window?

Lets assume that you own naughty donkey, which likes to jump over fence to visit your neighbours. To stop him you have bought higher fence and are planning to erect higher fence around the perimeter of your land. However, the place for fence is on a inclined plane and therefore the situation is little bit more complicated. What would be the best angle to erect the fence to make it most difficult for your donkey to jump over?

A carriage of mass $m$ travels in horizontal direction at speed $\textbf{v}$. In front of him is a „wooden bump“ of mass $M$ and height $h$, which slides on the horizontal plane without friction (figure 1). The carriage goes onto the bump. What conditions must be fulfilled for carriage to go over the bump? What will be the final velocity of the bump?