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Консультация № 129715
30.03.2008, 16:45
0.00 руб.
0
1
1
Здравствуйте, уважаемые эксперты, очень нужна Ваша помощь в решении этой задачи.
1,1
Две прямые дороги пересекаются под углом 60 градусов. От перекрестка по ним удаляются машины: одна со скоростью 60 км/ч, другая со скоростью 80 км/ч. Определить скорости, с которыми одна машина удаляется от другой. Перекресток машины прошли одновременно. Рассмотреть два возможных варианта.
Заранее спасибо :)
1,1
Две прямые дороги пересекаются под углом 60 градусов. От перекрестка по ним удаляются машины: одна со скоростью 60 км/ч, другая со скоростью 80 км/ч. Определить скорости, с которыми одна машина удаляется от другой. Перекресток машины прошли одновременно. Рассмотреть два возможных варианта.
Заранее спасибо :)
Обсуждение
04.04.2008, 13:45
общий
это ответ
Здравствуйте, Николай Фаворисович Басманов!
Спроектируем вектор скорости 80 км/ч на направление дороги, по которой 2-я машина удаляется от перекрестка со скоростью 60 км/ч. Проекция L равна 80*COS(60°) = 80*0.5 = 40 км/ч. В первом варианте вектор скорости удаления - это гипотенуза треугольника с катетами H = 80*SIN(60°) = 80*√(3/4) и (60 - L), во втором - с катетами H и (60 + L). Соответственно V<sub>1</sub> = √(H<sup>2</sup> + 20<sup>2</sup>), V<sub>2</sub> = √(H<sup>2</sup> + 100<sup>2</sup>). Ответ: 72.1 км/ч и 121.7 км/ч. (Надеюсь, приложенный файл с рисунком сможете открыть).
Спроектируем вектор скорости 80 км/ч на направление дороги, по которой 2-я машина удаляется от перекрестка со скоростью 60 км/ч. Проекция L равна 80*COS(60°) = 80*0.5 = 40 км/ч. В первом варианте вектор скорости удаления - это гипотенуза треугольника с катетами H = 80*SIN(60°) = 80*√(3/4) и (60 - L), во втором - с катетами H и (60 + L). Соответственно V<sub>1</sub> = √(H<sup>2</sup> + 20<sup>2</sup>), V<sub>2</sub> = √(H<sup>2</sup> + 100<sup>2</sup>). Ответ: 72.1 км/ч и 121.7 км/ч. (Надеюсь, приложенный файл с рисунком сможете открыть).
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