시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 364 304 269 84.062%

문제

특수 상대성 이론에서 가장 흥미를 불러일으키는 예측은 움직이는 물체의 시간이 느리게 간다는 것이다. 효과가 매우 작기 때문에 보통의 경우에는 이 사실을 인지하지 못한다. 하지만, 빛의 속도(초속 299,792,458미터)에 가깝게 움직인다면 효과를 느낄 수 있다.

시간 지연 현상은 쌍둥이 역설로 설명한다. 두 쌍둥이 A와 B가 어렸을 때, A 지구에 남아있고, B 빛의 속도에 가깝게 움직이는 우주선을 타게 된다. 50년이 지난 후에, B는 지구로 돌아오게 된다. 그동안 50살을 먹은 A는 몇 년 밖에 늙지 않은 B를 보고 큰 충격을 받게 된다.

두 쌍둥이가 느끼는 상대적인 시간은 아래와 같은 식으로 나타낼 수 있다.

\[t_{B} =\gamma  t_{A}\]

tB는 우주선을 탄 사람 B가 경험하는 시간이고, tA는 지구에 남아있는 A가 경험하는 시간이다. 변환 계수 γ는 다음과 같이 계산할 수 있다.

\[\gamma = \sqrt{1-\frac{v^{2}}{c^{2}}}\]

v는 우주선의 평균 속도이고, c는 빛의 속도이다. (v의 단위와 c의 단위는 같다)

예를 들어, v가 초속 259,620,268 미터인 경우에 γ = 0.5 (근사값) 이고, 지구에 있는 쌍둥이에게 2년의 시간이 지난 것은 우주선을 탄 쌍둥이가 1년이 지난 것과 같게된다.

tA와 tB가 주어졌을 때, 그러한 차이를 만들기 위해 필요한 우주선의 평균 속도를 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 두 실수로 이루어져 있고, tA와 tB이다. 항상 tA ≥ tB이며, 1.0 ... 100.0 범위를 가진다.

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

각 테스트 케이스에 대해서, 우주선의 평균 속도를 출력한다. 단위는 광속이며, 소수점 셋째 자리 까지 출력한다.

예제 입력 1

10.5 5.25
5 1
0 0

예제 출력 1

0.866
0.980
[{"problem_id":"4706","problem_lang":"0","title":"\uc30d\ub465\uc774 \uc5ed\uc124","description":"<p>\ud2b9\uc218 \uc0c1\ub300\uc131 \uc774\ub860\uc5d0\uc11c \uac00\uc7a5 \ud765\ubbf8\ub97c \ubd88\ub7ec\uc77c\uc73c\ud0a4\ub294 \uc608\uce21\uc740 \uc6c0\uc9c1\uc774\ub294 \ubb3c\uccb4\uc758 \uc2dc\uac04\uc774 \ub290\ub9ac\uac8c \uac04\ub2e4\ub294 \uac83\uc774\ub2e4. \ud6a8\uacfc\uac00 \ub9e4\uc6b0 \uc791\uae30 \ub54c\ubb38\uc5d0 \ubcf4\ud1b5\uc758 \uacbd\uc6b0\uc5d0\ub294 \uc774 \uc0ac\uc2e4\uc744 \uc778\uc9c0\ud558\uc9c0 \ubabb\ud55c\ub2e4. \ud558\uc9c0\ub9cc, \ube5b\uc758 \uc18d\ub3c4(\ucd08\uc18d 299,792,458\ubbf8\ud130)\uc5d0 \uac00\uae5d\uac8c \uc6c0\uc9c1\uc778\ub2e4\uba74 \ud6a8\uacfc\ub97c \ub290\ub084 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc2dc\uac04 \uc9c0\uc5f0 \ud604\uc0c1\uc740 \uc30d\ub465\uc774 \uc5ed\uc124\ub85c \uc124\uba85\ud55c\ub2e4. \ub450 \uc30d\ub465\uc774 A\uc640 B\uac00 \uc5b4\ub838\uc744 \ub54c, A \uc9c0\uad6c\uc5d0 \ub0a8\uc544\uc788\uace0, B \ube5b\uc758 \uc18d\ub3c4\uc5d0 \uac00\uae5d\uac8c \uc6c0\uc9c1\uc774\ub294 \uc6b0\uc8fc\uc120\uc744 \ud0c0\uac8c \ub41c\ub2e4. 50\ub144\uc774 \uc9c0\ub09c \ud6c4\uc5d0, B\ub294 \uc9c0\uad6c\ub85c \ub3cc\uc544\uc624\uac8c \ub41c\ub2e4. \uadf8\ub3d9\uc548 50\uc0b4\uc744 \uba39\uc740 A\ub294 \uba87 \ub144 \ubc16\uc5d0 \ub299\uc9c0 \uc54a\uc740 B\ub97c \ubcf4\uace0 \ud070 \ucda9\uaca9\uc744 \ubc1b\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub450 \uc30d\ub465\uc774\uac00 \ub290\ub07c\ub294 \uc0c1\ub300\uc801\uc778 \uc2dc\uac04\uc740 \uc544\ub798\uc640 \uac19\uc740 \uc2dd\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\\[t_{B} =\\gamma &nbsp;t_{A}\\]<\/p>\r\n\r\n<p>t<sub>B<\/sub>\ub294 \uc6b0\uc8fc\uc120\uc744 \ud0c4 \uc0ac\ub78c B\uac00 \uacbd\ud5d8\ud558\ub294 \uc2dc\uac04\uc774\uace0, t<sub>A<\/sub>\ub294 \uc9c0\uad6c\uc5d0 \ub0a8\uc544\uc788\ub294 A\uac00 \uacbd\ud5d8\ud558\ub294 \uc2dc\uac04\uc774\ub2e4. \ubcc0\ud658 \uacc4\uc218 &gamma;\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\\[\\gamma = \\sqrt{1-\\frac{v^{2}}{c^{2}}}\\]<\/p>\r\n\r\n<p>v\ub294 \uc6b0\uc8fc\uc120\uc758 \ud3c9\uade0 \uc18d\ub3c4\uc774\uace0, c\ub294 \ube5b\uc758 \uc18d\ub3c4\uc774\ub2e4. (v\uc758 \ub2e8\uc704\uc640 c\uc758 \ub2e8\uc704\ub294 \uac19\ub2e4)<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, v\uac00 \ucd08\uc18d 259,620,268 \ubbf8\ud130\uc778 \uacbd\uc6b0\uc5d0 &gamma; = 0.5 (\uadfc\uc0ac\uac12) \uc774\uace0, \uc9c0\uad6c\uc5d0 \uc788\ub294 \uc30d\ub465\uc774\uc5d0\uac8c 2\ub144\uc758 \uc2dc\uac04\uc774 \uc9c0\ub09c \uac83\uc740 \uc6b0\uc8fc\uc120\uc744 \ud0c4 \uc30d\ub465\uc774\uac00 1\ub144\uc774 \uc9c0\ub09c \uac83\uacfc \uac19\uac8c\ub41c\ub2e4.<\/p>\r\n\r\n<p>t<sub>A<\/sub>\uc640 t<sub>B<\/sub>\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uadf8\ub7ec\ud55c \ucc28\uc774\ub97c \ub9cc\ub4e4\uae30 \uc704\ud574 \ud544\uc694\ud55c \uc6b0\uc8fc\uc120\uc758 \ud3c9\uade0 \uc18d\ub3c4\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub450 \uc2e4\uc218\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, t<sub>A<\/sub>\uc640 t<sub>B<\/sub>\uc774\ub2e4. \ud56d\uc0c1 t<sub>A<\/sub> &ge; t<sub>B<\/sub>\uc774\uba70, 1.0 ... 100.0 \ubc94\uc704\ub97c \uac00\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uc6b0\uc8fc\uc120\uc758 \ud3c9\uade0 \uc18d\ub3c4\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub2e8\uc704\ub294 \uad11\uc18d\uc774\uba70, \uc18c\uc218\uc810 \uc14b\uc9f8 \uc790\ub9ac \uae4c\uc9c0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4706","problem_lang":"1","title":"A Most Ingenious Pair a\u2019 Twins","description":"<p>One of the intriguing predictions of the Special Theory of Relativity is that time actually slows down for moving objects. We don&rsquo;t normally notice this, because the effect is tiny until you get up to a good-sized fraction of the speed of light (299,792,458 meters per second). So it&rsquo;s not something you will notice on your average drive to and from the supermarket.<\/p>\r\n\r\n<p>The implications of this slowdown of time is often illustrated by the so-called Twins Paradox. Imagine two twins, both young adults, one of whom remains on Earth while the other boards a rocket ship that travels at nearly the speed of light for 50 years before returning to Earth. The Earth-bound twin, now a senior citizen after 50 years, is astounded to greet the traveler who has aged only a few years.<\/p>\r\n\r\n<p>The relative time experienced by the two twins is given by the formula<\/p>\r\n\r\n<p>\\[t_{r} =\\gamma &nbsp;t_{e}\\]<\/p>\r\n\r\n<p>where t<sub>r<\/sub> is the time experienced by the twin on the rocket and t<sub>e<\/sub> is the amount of time experienced by the twin who remains on Earth. The conversion factor &gamma; is given by<\/p>\r\n\r\n<p>\\[\\gamma = \\sqrt{1-\\frac{v^{2}}{c^{2}}}\\]<\/p>\r\n\r\n<p>where v is the average velocity of the rocket and c is the speed of light (expressed in the same units as v).<\/p>\r\n\r\n<p>For example, if v is 259,620,268 meters per second, then &gamma; = 0.5 (approximately) and the Earth-bound twin experiences 2 years for every year experienced by the traveler.<\/p>\r\n\r\n<p>Write a program to determine, for two target values of t<sub>e<\/sub> and t<sub>r<\/sub>, the average velocity that the rocket would need to travel to produce that difference in time experienced by the two twins.<\/p>\r\n","input":"<p>Input will consist of one or more datasets. Each dataset will consist of two \ufb02oating point values on a single line. These values will denote t<sub>e<\/sub> and t<sub>r<\/sub>, respectively, expressed in years. You are guaranteed that t<sub>e<\/sub> &ge; t<sub>r<\/sub> and that both times will be in the range 1.0. . .100.0, inclusive.<\/p>\r\n\r\n<p>End of input is indicated by a line containing two zeros.<\/p>\r\n","output":"<p>For each dataset, print a single line of output containing the desired velocity, expressed in lightyears per year, printed to a precision of 3 decimals.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]