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Консультация № 77694
09.03.2007, 21:05
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Никак не могу решить эту задачу. Поэтому искренне прошу оказать мне помощь!
Итак уважаемые знатоки внимание вопрос!
Два тела при движении по окружности в одном и том же направлении встречаются каждые 56мин. Если бы они двигались с теми же скоростями в противоположных направлениях, то встречались бы каждые 8мин. При движении в противоположных направлениях расстояние между сближающимися телами уменьшилось на 14м за 24 с. Найдите скорость каждого тела.
Спасибо за внимание. Если вы ответите, буду очень благодарен!
Итак уважаемые знатоки внимание вопрос!
Два тела при движении по окружности в одном и том же направлении встречаются каждые 56мин. Если бы они двигались с теми же скоростями в противоположных направлениях, то встречались бы каждые 8мин. При движении в противоположных направлениях расстояние между сближающимися телами уменьшилось на 14м за 24 с. Найдите скорость каждого тела.
Спасибо за внимание. Если вы ответите, буду очень благодарен!
Обсуждение
Неизвестный
09.03.2007, 21:15
общий
это ответ
Здравствуйте, Timon!
Обозначим скорости как x и y; х - большая скорость
Из последнего условия найдем суммарную скорость:
x+y=14*60/24=35 м/мин
Из второго - длину окружности
8*35=280м
Из первого - разность скоростей
х-у=280/56=5 м/мин
Сложив первое и последнее уравнения получим
2х=40
Откуда х=20 у=15
Обозначим скорости как x и y; х - большая скорость
Из последнего условия найдем суммарную скорость:
x+y=14*60/24=35 м/мин
Из второго - длину окружности
8*35=280м
Из первого - разность скоростей
х-у=280/56=5 м/мин
Сложив первое и последнее уравнения получим
2х=40
Откуда х=20 у=15
Неизвестный
10.03.2007, 01:10
общий
это ответ
Здравствуйте, Timon!По моему это задача по физике ,а не по математике.Будем считать что ускорение обеих тел равно нулю.Пусть L - длина данной окружности.Наверное,легче искать линейную скорость,а не угловую.Х-скорсть одного тела,Y-скорость другого,пусть X-Y>0.За 56 минут тело с большей скоростью проходит круг догоняя более медленное тело.Значит (Х-Y)*56 мин.=L.По второму пункту тела проходят каждый свою часть круга(опять-таки круг),итого получаем:(Х+У)м/мин*8мин=L.Используя 3 условие находим:(Х+У)м/мин*24ceк=14м.
24сек=2/5минуты.Так получилась система из 3 уравнений.
(Х-У)*56=L
(X+Y)*8=L => X+Y=14*5/2=35 => Подставим "Х+У=35" во второе уравнение.
(X+Y)*(2/5)=14
Получается L=35*8=280.Итак L = 280 метров.Составляем новую систему уравнений.
Х-У=L/56=280/56=5
X+Y=35
Сложив их - получаем : 2*Х=40.Отсюда находим Х=20 м/мин. и У=15м/мин.
Скорость принято измерять в метрах на секунду-переведем полученые величины:1минута=60секунд.
Ответ:Х = 0,3 м/с ; У = 0,25 м/с .
P.S.Павла Владимировича исправить не в чем.
С уважением Айболит.
24сек=2/5минуты.Так получилась система из 3 уравнений.
(Х-У)*56=L
(X+Y)*8=L => X+Y=14*5/2=35 => Подставим "Х+У=35" во второе уравнение.
(X+Y)*(2/5)=14
Получается L=35*8=280.Итак L = 280 метров.Составляем новую систему уравнений.
Х-У=L/56=280/56=5
X+Y=35
Сложив их - получаем : 2*Х=40.Отсюда находим Х=20 м/мин. и У=15м/мин.
Скорость принято измерять в метрах на секунду-переведем полученые величины:1минута=60секунд.
Ответ:Х = 0,3 м/с ; У = 0,25 м/с .
P.S.Павла Владимировича исправить не в чем.
С уважением Айболит.
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