Question

Dois corredores partem em ssntidos opostos e no mesmo instante,dos extremos de uma pista retilinear de 600m.suas velocidades são 8,5 m/s e 6,5 m/s caucule depois de quanto tempo e distancia entre eles e de 450 m

Answer 1

$Ola'~~~\mathbf{Eduarda} \\ \\ Vamos~ilustrar~para~poder ~entender~vejamos: \\ \\ \xrightarrow{V=8,5m/s}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\xleftarrow{V=6,5m/s}\\ \underline{\textcircled{a}~~~~~~~~~~~~~~~~~~~~~~\textcircled{a}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textcircled{b}~~~~~~~~~~\textcircled{b}} \\ ~0m~~~~~~~~~~~~~~~~~~~~~S_1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~S_2~~~~~~~~~600m \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~\underline{|~~~~~~~~~~~~450m~~~~~~~~~~~~~|} \\ ~~~$


$Usaremos~uma~\acute{u} nica~f\acute{o}rmula~que~e'~\boxed{S=S_0+V.t} \\ \\~~~~~~~~~~~~~~~~~~~~~~ corredores \\ ~~~~~~~~~~~~\textcircled{a}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textcircled{b} \\ Dados:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Dados: \\ S_0=0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~S_0=600m\\ S_1=?~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~S_2=? \\ t=? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t=?\\ V=8,5m/s~~~~~~~~~~~~~~~~~~~~~~~~~~V=6,5m/s \\ \\ Substituindo~dados~na~f\acute{o}mula~temos:$

$\boxed{S_1=8,5t}~---\ \textgreater \ (I)~~~~\boxed{S_2=600-6,5t} ~---\ \textgreater \ (II) \\ \\ Nos~disse~que~la~distancia~entre~eles~e'~de~450m~oseja: \\ \boxed{S_2-S_1=450m}~----\ \textgreater \ (III) \\ \\ Substituindo~(I)~e~(II)~em~(III)~temos: \\ 600-6,5t-8,5t=450 \\ -15t=450-600 \\ -15t=-150 \\~~~~~ t= \frac{-150}{-15} \\ ~~~~~\boxed{\boxed{t=10s}}~--\ \textgreater \ tempo~para~fazer~entre~eles~450m$

$================================== \\ Agora~calculemos~que~distancia~cada~um~deles~fez, vejamos: \\ S_1=8,5t~~--\ \textgreater \ sabemos[t=10s] \\ S_1=8,5(10) \\ \boxed{d=85m}~~--\ \textgreater \ corredor~\textcircled{a} \\ \\ S_2=600-6,5t \\ S_2=600-6,5(10) \\ S_2=600-65 \\ S_2=535m \\ d=600-535 \\ \boxed{\boxed{d=65m}}~--\ \textgreater \ corredor~\textcircled{b } \\ \\ \mathbb{iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$