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Консультация № 198480
07.05.2020, 16:48
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Велосипедист и автомобиль подъезжают по перпендикулярным дорогам к перекрёстку. Когда велосипедист проезжал перекрёсток, автомобиль ещё не доехал до перекрёстка 100 м. Какое время после этого пройдёт до момента, когда велосипедист и автомобиль окажутся на минимальном расстоянии, если их скорости постоянны и равны V1=7 м/с у велосипедиста и V2=24 м/с у автомобиля?
Спасибо!
Велосипедист и автомобиль подъезжают по перпендикулярным дорогам к перекрёстку. Когда велосипедист проезжал перекрёсток, автомобиль ещё не доехал до перекрёстка 100 м. Какое время после этого пройдёт до момента, когда велосипедист и автомобиль окажутся на минимальном расстоянии, если их скорости постоянны и равны V1=7 м/с у велосипедиста и V2=24 м/с у автомобиля?
Спасибо!
Обсуждение
08.05.2020, 20:11
общий
это ответ
Здравствуйте, suvorov.shool@mail.ru!
Пусть велосипедист движется по оси "x" из точки x=0,y=0,
а автомобиль по оси "y" из точки x=0, y=-100м
декартовой системы координат.
Уравнения движения велосипедиста и автомобиля:
Квадрат расстояния между ними:
Для нахождения минимума приравняем производную квадрата расстояния по времени к нулю:
При этом координаты участников движения и расстояние между ними (метров):
Пусть велосипедист движется по оси "x" из точки x=0,y=0,
а автомобиль по оси "y" из точки x=0, y=-100м
декартовой системы координат.
Уравнения движения велосипедиста и автомобиля:
Квадрат расстояния между ними:
Для нахождения минимума приравняем производную квадрата расстояния по времени к нулю:
При этом координаты участников движения и расстояние между ними (метров):
5
Об авторе:
Понеже не словес красных бог слушает, но дел наших хощет
Понеже не словес красных бог слушает, но дел наших хощет
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