수학동아 - 폴리매스

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함께 풀고 싶은 문제

나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.

[문장제 문제&개념응용] 지구의 모양을 알아내는 법 응용

아인수타인 2021.02.15 04:04 조회 435

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

학교에서 지구의 모양이 둥글다는 증거 중 무엇이 있다고 했는가? 기타 여러 사항들이 더 있을진 몰라도 아마 항구에 들어오는 배의 모습을 보는 건 꼭 있을 것이다. 항구로 들어오는 배를 보면 배 위쪽부터 보이다가 점차 아래쪽이 보인다. 그런데 사실 이 정보만 보고 지구가 둥글다는 가능성을 높여 줄 순 있어도, 확정지을 순 없다. 혹시 지구가 원기둥 모양일지 어떻게 아는가? 원기둥의 옆면이어도 배의 위쪽부터 보일 것이다.

(1) 항구로 들어오는 배의 아래쪽부터 보이는 행성의 모양을 그려보아라.

(2) 만약 행성이 구와 위상동형이어야 한다면 (1)번처럼 되는 것이 가능할까? 증명해보아라.

(3) 배가 안 보이다가 어느 순간 갑자기 전체가 보이는 행성의 모양을 그려보아라.

(4(출제자도 미해결)) 지구처럼 구 모양이지만 반지름이 겨우 3m인 혹성이 있고, 이 행성에서 키 1m인 어린왕자가 항구로 들어오는 높이 1m의 배를 본다~~(그런데 이렇게 작은 행성에서 배가 돌아다닐 필요가 있나?)~~. 어린왕자가 관찰했을 때, 배가 일정한 속력으로 위쪽부터 보인다고 한다. 그러면 배가 들어오는 속력의 그래프를 그려라. 단, 배가 보이기 시작하는 때를 $t=0$ 으로 본다.

(5(출제자도 미해결)) 반대로 배가 일정한 속력으로 들어온다면 어린왕자가 볼 때 배가 보이는 속력(즉, 지평선과 배가 만나는 지점의 수직방향 속력)의 그래프를 그려라. 그 외의 조건은 4번 문제와 완벽히 같다.

이전글 루트 루트 루트 루트...

다음글 아주 단순히 피보나치 수열의 최대공약수를 구하는 것일 뿐인 문제

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