Una furgoneta circula por una carretera a 55km/h. Diez km atrás , un coche circula en el mismo sentido a 85km/h ¿ En cuanto tiempo alcanzará

Question

Una furgoneta circula por una carretera a 55km/h. Diez km atrás , un coche circula en el mismo sentido a 85km/h ¿ En cuanto tiempo alcanzará el coche a la furgoneta? ¿A qué distancia se producirá el encuentro?

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Khải Quang 1 year 2021-09-03T19:53:20+00:00 1 Answers 75 views 0

Answers ( )

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    2021-09-03T19:55:10+00:00

    Answer:

    t = 0.33h = 1200s

    x = 18.33 km

    Explanation:

    If the origin of coordinates is at the second car, you can write the following equations for both cars:

    car 1:

    [tex]x=x_o+v_1t[/tex]    (1)

    xo = 10 km

    v1 = 55km/h

    car 2:

    [tex]x’=v_2t[/tex]    (2)

    v2 = 85km/h

    For a specific value of time t the positions of both cars are equal, that is, x=x’. You equal equations (1) and (2) and solve for t:

    [tex]x=x’\\\\x_o+v_1t=v_2t\\\\(v_2-v_1)t=x_o\\\\t=\frac{x_o}{v_2-v_1}[/tex]

    [tex]t=\frac{10km}{85km/h-55km/h}=0.33h*\frac{3600s}{1h}=1200s[/tex]

    The position in which both cars coincides is:

    [tex]x=(55km/h)(0.33h)=18.33km[/tex]

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