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Здравствуйте! Прошу помощи в следующем вопросе: Модули двух сил, действующих на материальную точку под прямым углом, и модуль их равнодействующей составляют арифметическую прогрессию. Определить, в каком отношении находятся модули сил.
Вопрос связан с физикой, но так как книга, из которой взято данное задание, по алгебре, то решил задать вопрос здесь. {F =F1 + d(F-1) {F = F2 + d(F-1)
Где F - равнодействующая сила. F1 и F2 - две сила. //------------------------------------ Пожалуйста, если, возможно, то с пояснениями, я не могу понять как это решить, хотя, видимо, тема за 7 класс, но....))
Книга автора по фамилии Сканави. Мне не решение нужно, я хочу разобраться, как подобное решать, то что задача из физики, я понял, о чём написал в первом посте.
Алгебра. Сборник задач по математике для поступающих во ВТУЗы. (М.И. Сканави. 1992 год).
Всё что я мог придумать я написал в первом посте темы. Не знаю какие там ещё могут быть отношения. Чтобы получить равнодействующую силу нужно сложить силы, в данном случае F1 и F2, насколько я понимаю. Не совсем мне ясна формулировка "Модули двух сил, действующих на материальную точку под прямым углом", если представить систему координат, взять некую точку(которая и будет материальной) и отложить два вектора под прямым углом это и будут те самые силы, так? Или..., П.С. Надеюсь, что более или менее ясно изложил.
Тогда, если я всё правильно выше изложил это сложение векторов по правилу прямоугольника. А что дальше то... Вот попытался наглядно показать, как я вижу ситуацию. Вот
Я не знаю, что тут можно ещё добавить a + b = c, если a и b это исходные вектора, а 'c', соответственно, результат. (ax; ay) + (bx; by) = (ax+bx; ay+by)
- напоминает т. Пифагора или это я не в ту степь направился? А зачем квадрат? Это из-за условия, где сказано о модулях? Хоть тресни не пойму, как они составляют арифметическую прогрессию...
Я так понимаю - это шутка...., вы серьёзно считаете, что ещё пять суток стоит крапеть над этой задачей, может больше конкретики, глядишь я и пойму, но без наглядного примера, точно, не пойму.
Я намекнул Вам достаточно. Обращайтесь к модераторам с просьбой о продлении срока консультации или смиритесь с тем, что и эту задачу самостоятельно Вы не решили. В этом нет плохого.
Ответ: прогрессия предполагает определённые соотношения между её членами. Выявить и использовать эти соотношения, а также другие, согласно условию задачи, -- по сути дела, и значит решить задачу.
Поскольку мои попытки намекнуть Вам в мини-форуме консультации, что нужно сделать, чтобы решить задачу, оказались безуспешными, постольку я привожу своё решение задачи ниже. Несмотря на то, что Вы сообщили:
Пусть -- длины сторон прямоугольного треугольника сил, -- разность арифметической прогрессии. Тогда и по теореме Пифагора имеем
Решая последнее уравнение относительно неизвестной величины получим
(не подходит, потому что рассматриваемая арифметическая прогрессия возрастающая),
Значит, искомое отношение модулей сил составляет
5
Об авторе:
Facta loquuntur.
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