Futebol e Física
Autor: Kleber Nogueira | Publicado: 2012-08-01T12:31:00-07:00

Em época de olimpíadas, vamos falar sobre um
esporte: Futebol. E claro com um pouco de Física. Os lançamentos, como o tiro
de meta ou cruzamentos, é uma possibilidade de analisar o futebol através da
física, onde tais lançamentos são analisados nos movimentos bidimensionais
denominados Lançamento Obliquo. Esse tipo de analise é corriqueiro em
vestibulares e no ultimo vestibular de meio do ano da Vunesp 2012, na prova de
Conhecimentos Gerais, essa questão voltou a cair.



Questão 77


O gol que Pelé não fez





Na copa de 1970, na partida entre Brasil e Tchecoslováquia,


Pelé pega a bola um pouco antes do meio de campo, vê o


goleiro tcheco adiantado, e arrisca um chute que entrou para a


história do futebol brasileiro. No início do lance, a bola parte


do solo com velocidade de 108 km/h (30 m/s), e três segundos


depois toca novamente o solo atrás da linha de fundo, depois de


descrever uma parábola no ar e passar rente à trave, para alívio


do assustado goleiro.
Na figura vemos uma simulação do chute de Pelé.






Considerando que o vetor velocidade inicial da bola após o chute de Pelé
fazia um ângulo de 30º com a horizontal (sen30º = 0,50 e cos30º = 0,85) e
desconsiderando a resistência do ar e a rotação da bola, pode-se afirmar que a
distância horizontal entre o ponto de onde a bola partiu do solo depois do
chute e o ponto onde ela tocou o solo atrás da linha de fundo era, em metros,
um valor mais próximo de:


(A) 52,0.


(B) 64,5.


(C) 76,5.


(D) 80,4.


(E) 86,6.


Resolução:
Nesta questão temos um típico lançamento obliquo onde pede-se para
calcular o alcance máximo. Do estudo&nbsp;da cinemática, temos a relação:





Do enunciado da questão temos:

V0=30m/s;

Θ=30°

sen30º = 0,50 e cos30º =
0,85

g=10m/s²








 
 
  
  
  
  
  
  
  
  
  
  
  
  
 
 
 
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