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4. Series 19. Year - 3. balloons on the merry go round


Two balloons are fixed on a single string of length $l$. The string is threaded through a horizontal hollow tube of length $L$. Both balloons weight approximately the same, however one is slightly heavier.

The tube starts spinning around vertical axis. What is the optimum position of this axis for the horizontal distance between balloons to be the biggest?

Vymyslel Jirka a Kájínek špatně pochopil.

4. Series 19. Year - 4. wedding of two balloons

At the wedding ceremony the new couple kisses. For balloons it means to connect it orifices to connect the inside gas into a single One. Describe what would happened after the orifices are connected. Do not forget that all balloons have the same parameters.

Navrhl Petr Sýkora.

5. Series 18. Year - P. faster than water

Is it possible for the boat to move faster than the water in the river? Justify you answer and assume laminar flow.

Kapicova úloha

3. Series 18. Year - 4. with the glider over the channel


One of well known glider pilots decided to cross the British Channel. In Calais he rented a plane to took him to the height h = 3 km and from there glided directly to England. As every pilot knows, glider's downward speed $v_{kles}$ depends on the forward speed $v_{dop}$ as in the image 2. What is the optimum speed to achieve the longest flight? When the pilot is 3/4 of its way to England strong wind starts to blow in direction from England to France at the speed 10 $ms^{-1}$. What is the optimum speed now? What is the maximum wind speed which allows him to come to England? And what is the sped of wind to allow for the safe return to France?

Vymyslel Matouš.

2. Series 18. Year - 1. Moses's miracle

Moses came to the Red Sea and said: „Lets the water open and let us go by dry foot to the land of promise.“ Then he entered into waves and they opened. What was the Moses's force, if he moved Jews over Red Sea. Assuming the sea to be 1 wide and 20 deep.

Vymyslel Jarda Trnka při čtení Bible.

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