RMPh 2011, Експеримент — Задача 1

Romanian Master of Mathematics and Sciences 2011 Physics Section · 8 т.

Условие

It is now the advent of the space age and cosmic flight is the norm. Convoys of spaceships crisscross the empty space between Earth and remote colonies.
You are the commander of such a convoy, consisting of five rockets labeled from A to E in marching order. This is your very first mission but fortunately you don’t have many responsibilities, since the entire cruise is set up to the last detail right from takeoff. There is even no need of a meter reading the cruising speed, because there are absolutely no nearby celestial bodies whatsoever to be taken as reference frame, and anyway the speed changes only at departure and arrival.

All you are provided with is a set of absolutely accurate and synchronized clocks, one for each rocket, and you also know the distance between the rockets, the same for each two consecutive ones. We will adopt this distance as length unit (“l.u.”) and the units used in the readings of the clocks as time unit (“t.u.”). (It is also important to stress the obvious fact that you cannot check any two of your clocks simultaneously.)

At some time during your journey you encounter a convoy absolutely identical in all respects (number of rockets, distance between them, magnitude of the velocity, and so on), returning to Earth from the same destination you are heading to. It is your duty to write down in the captain’s log the exact time at which the other rockets (labeled from 1 to 5) pass by your ships. Here is the table documenting these events.

The times written in red refer to another phenomenon recorded at the same moment as the passage of the incoming rockets.
By analyzing the above data, you are in a position to determine several things:

a. The relative velocity $v_{\mathrm{rel}}$ of the other convoy with respect to yours. [1 т.]

b. The velocity $v_{\mathrm{abs}}$ of both the convoys with respect to Earth. [2 т.]

c. The relative velocity $u_{\mathrm{rel}}$ of the undetermined phenomenon with respect to you. [1 т.]

d. The velocity $u_{\mathrm{abs}}$ of the undetermined phenomenon with respect to Earth. [1 т.]

e. Determine the nature of the phenomenon and suggest an explanation for its presence. [1 т.]

f. The table documenting these events as they are recorded in the captain’s log of the other convoy, assuming that it starts also at time 00:00. Please use the table below as you answer sheet for this point. Please write in red the two times corresponding to the undetermined phenomenon in the first table.

[2 т.]

Отговори

Решение

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Оригинал в Архива: exp.pdf · официални решения: exp_sol.pdf