[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 131
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а про полпени лень думать?
I don't have a proper reference book handy. If you google it, you might get an answer and it won't be fair. The result is a moral and material stalemate... :)
Laziness, of course, if google is at hand. Here's about bisectors much more unladylike, almost native.
Да :)
ChachaGames, MetaDriver, вы правы. Не вкрутится. Как показывает моя практика, примерно 2\3 людей отвечают на этот вопрос неправильно.
Shall I say why 2/3?
Because 1/3 says "clockwise", 1/3 "anti-clockwise" and 1/3 gives the right answer... almost like a dinosaur problem:)))
Task No. 12
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A hole is drilled into the planet Earth (hypothetically). One end of the hole is in city M, the other end is approximately on the opposite side of the Earth - in city N. A brick is thrown into the hole (free fall). The exact distance between cities M and N is unknown.
Question: How long will it take for the brick to fly from city M to city N. The air resistance is completely neglected. Also neglect the collisions of the brick with the Earth.
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Задача № 12
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В планете Земля просверлили отверстие (гипотетически). Один конец отверстия находится в городе М, другой - примерно на противоположной стороне Земли - в городе N. В отверстие бросили кирпич (свободное падение). Точное расстояние между городами M и N неизвестно.
Вопрос: за какое время кирпич долетит из города М до города N. Сопротивлением воздуха полностью пренебречь. Столкновениями кирпича с Землёй также пренебречь.
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In a school physics course, it is proved that the acceleration of free fall inside a homogeneous ball is directly proportional to the distance from the centre x. Knowing the radius of the Earth R and y.s.p. on the surface g0, we write down the equation of motion of the brick:
x''=-g0*x/R
(minus takes into account the direction of the acceleration vector towards the centre)
Again, for those who studied physics at school it will be easy to remember that this is the equation of the harmonic oscillator which makes oscillations from one extreme point to another and back with period
T=2*pi*sqrt(R/g0).
The time it takes the brick to reach the enemies is equal to half of the period.
So how many hours or minutes would that be?
Сопротивлением воздуха полностью пренебречь. Столкновениями кирпича с Землёй также пренебречь
If you neglect these parameters only, it will not get there at all :-)
Если пренебречь только этими параметрами, то он вообще туда недолетит :-)
It's bound to dangle back and forth :)