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수학동아 - 폴리매스
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함께 풀고 싶은 문제
나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.
[문장제 문제&개념응용] 늦잠의 응징
우럭 2021.01.16 09:10 조회 524

원파가 더 자는 걸 참고 보고만 있을 수 없던 라임은

또 다른 방책을 세우려고 한다. (전 문제 참고)

이번엔 소리가 아닌, 진동으로 깨우려고 한다.

다행히도 원파의 침대 매트리스과 원파의 질량을 합친만큼의 질량은 라임이 들 수 있다.

그래서, 이번에는 원파를 침대를 흔들어 깨우려고 한다.

원파를 빠르고, 잘 깨우기 위하여 라임은 이 침대를 파장의 모형으로 해서 흔드려고 한다.

원파의 기상함수 f(x)는 라임이 흔드는 침대의 파장 W에 비례하고,

진동수인 f에 대해 제곱으로 비례한다.

그러나 라임도 힘이 들기 마련, W = f = 1인 조건에서 지속시간 64초를 기준으로

지속시간은 파장 W에 3배로 반비례, 진동수 f에 대해 반비례한다.

원파의 침대 길이는 2.4m이고, 기상함수의 비례상수는 2라고 할때,

t * f(x)의 최댓값은 60초 동안 얼마인가?

[단 진동수의 비례상수는 1이라고 한다.]

 

 

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