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Exercício de Estratégia do cálculo integral em um planejamento de segurança.

por Rodrigo Muzy (UVA 2020) Difícil Saturday, March 14th, 2020

Exercício:

Muitas vezes é fundamental avaliar previamente o alcance dos impactos de uma intervenção que cause abalos a estruturas físicas, como é o caso de explosões e implosões.

Durante a explosão de uma mina, uma pedra pesada pode ser atirada para
cima a partir do solo. O geólogo responsável, pela explosão da Mina X estimou que a velocidade da pedra, em qualquer instante durante o seu movimento, pode ser descrita por

v(t) = 150 – 30t pés/s.

A empresa responsável pelo procedimento de explosão levará até a mina uma equipe formada por mineiros e um engenheiro de produção, responsável pela segurança do processo, planejado em conjunto com o geólogo, e também pela segurança dos trabalhadores.

Para que os mineiros possam pernoitar próximos à mina, será montada uma estrutura provisória, e o engenheiro devem indicar a partir de quantos metros da mina será seguro instalar esta estrutura, de forma que este tipo de pedra pesada não alcance a estrutura. Um dos critérios adotados é o que define que qualquer abrigo deve estar localizado a um raio de pelo menos 500 metros além da maior distância que pedras pesadas podem cair em relação à mina, durante uma explosão.

Qual deve ser a menor distância, em relação à mina, que a estrutura para pernoite dos mineiros deve ser instalada?

Faça as seguintes análises, considerando uma pedra pesada, determinando:

1.      O deslocamento da pedra durante o período de tempo 0< < 8.

 

2.      A distância total percorrida pela pedra durante esse período de tempo.

 

3.      A altura máxima atingida pela pedra, usando derivada.

 

4.      A maior distância que a pedra pode cair em relação à mina.

Informações Adicionais:


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