1. Series 34. Year

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(3 points)1. almost stopped light

Find the refractive index of a transparent plane-parallel plate of thickness $d=1 \mathrm{cm}$, such that it will take one year for the light to pass through it. Discuss whether such a situation is possible.

(3 points)2.

Carl's car, going at the initial speed of $v_0$, can stop at a distance $s_0$ with the constant braking force $F_0$. How many times will the braking distance increase if the initial speed doubles if the braking force stays the same? How many times must the braking force be for the car to stop at distance $s_0$ with the speed $2v_0$?

(5 points)3. cycling anemometer

Vašek rides his bicycle in windy weather. When he rides straight with the velocity $v = 10 \mathrm{km\cdot h^{-1}}$, he measures that the wind blows at an angle $25\dg $ from the direction of Vašek's direction of travel. When he accelerates to $v' = 20 \mathrm{km\cdot h^{-1}}$, the angle is only $15\dg $. Find the velocity and direction of the wind with respect to stationary observer.

(8 points)4. solar sail

A solar sail with the surface $S = 500 \mathrm{m^2}$ and area density $\sigma =1,4 \mathrm{kg\cdot m^{-2}}$ is located in the distance of $0,8 \mathrm{au}$ from the Sun. What force does the solar radiation act on the sail at the beginning of the sail's motion? What is the acceleration of the sail at that moment? The luminosity of the Sun is $L_{\odot } =3,826 \cdot 10^{26} \mathrm{W}$. Assume that the radiation approaches the sail from perpendicular direction and scatters elastically. Hint: We recommend to find acceleration for small initial velocity $v_0$ and then let $v_0 = 0$.

(8 points)5. how to put your beanie on sigle-handily

Let us have a ball with the radius $R$ and a circular massless rubber band with the radius $r_0$ and stiffness $k$, while $r_0 < R$. Coefficient of friction between the band and the ball is $f$. Find conditions which ensure that it is possible to stretch the band over the ball single-handily (i.e. we are allowed to touch the band in only one point.

To keep it simple assume that the band is elastic only in the tangential direction (so it is planar).

(10 points)P. Will we survive in vacuum?

Different movies create different conceptions of what and how fast happens when a space suit suddenly gets torn. Some of them are even contradictory. Explain, what is most likely to happen, if a healthy person finds himself unprotected in a vacuum. What phenomenon is most likely to cause death first?

(13 points)E. impact-y

Measure the dependence of the diameter of a crater, created by the impact of a stone into a suitable sandpit, on the weight of the stone and the height it is released from. Does the size of the crater depend only on the energy of the impact? Dry sand is recommended for this measurement.

(10 points)S.

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