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kicyunya [14]
3 years ago
9

12. A las 10 de la mañana Elena sale a 100 Km/h de una ciudad A con dirección a Madrid. A la misma hora sale Javier desde otra c

iudad B que situada en la misma dirección que A y lo hace a una velocidad de 60 Km/h también con dirección a Madrid. Sabiendo que la distancia en carretera entre A y B es de 132 Km, y suponiendo que los dos van a una velocidad constante todo el camino, contesta a las siguientes preguntas:
a) ¿Qué tiempo tardarán en encontrarse Elena y Javier?
b) ¿Qué hora será cuando se encuentren?
c) ¿Qué distancia habrá recorrido cada uno de ellos en ese momento?
Physics
1 answer:
Klio2033 [76]3 years ago
6 0

Answer:

a) t = 3.3 [h]

b ) Hora = 13:18 o 1:18 [pm]

c) x = 327.79 [km/h] (Elena)

x = 196.6 [km] (Javier)

Explanation:

Para poder solucionar este problema debemos hacer un planteamiento inicial de ubicacion de las ciudades, este planteamiento nos ayudara a entender el problema de una manera mas facil.

Tenemos las ciudades A & B y la ciudad de Madrid que esta a una distancia x con respecto de B, (ver esquema adjunto).

De manera logica debemos deducir que la Ciudad A debe estar mas lejos de Madrid que la ciudad B de la misma Madrid, ya que en caso contrario Javier nunca alcanzara a Elena, ya que Elena va mas rapido que Javier.

a) Ahora debemos de utilizar la siguiene ecuacion de la cinematica, cuando los cuerpos se mueven a velocidad constante.

x=x_{o}+v*t

Donde:

x -xo = Distancia entre el punto inicial y punto final.

v = velocidad [m/s]

t = tiempo [s]

Debemos convertir las velocidades de kilometros por hora a metros por segundo.

100 [\frac{km}{h} ]*1[\frac{h}{3600s}]*1000[\frac{m}{1km} ] = 27.77[m/s]\\60[\frac{km}{h} ]*1[\frac{h}{3600s}]*1000[\frac{m}{1km} ] = 16.66[m/s]

Seguidamente formulamos una ecuacion por cada movimiento, luego debemos igualar estas ecuaciones en funcion de la variable x que sera el punto donde se encuentren ambas personas.

<u>Para Elena</u>

(132000+x) = 27.77*t\\x = 27.77*t - 132000

<u>Para Javier</u>

<u />x - xo = 16.66*t\\xo = 0\\x = 16.66*t<u />

Igualamos las variables x de ambas ecuaciones.

16.66*t = 27.77*t -132000\\27.77*t - 16.66*t = 132000\\11.11*t = 132000\\t = 11880.83 [s] = 3.3 [h]

b) La hora facilmente se puede encontrar sumando el tiempo con las 10:00am

hora = 10 + 3 = 13 [hrs]

La parte decimal debe convertirse a tiempo.

0.3 [hr]*60[\frac{min}{1hr} ]= 18 min

Hora = 13:18 o 1:18 [pm]

c) Para encontrar estas distancias utilizamos el tiempo encontrado en el item a.

<u>Para Elena</u>

x = v*t\\x = 27.77*11800.83 = 327791.6 [m] = 327.79 [km]\\

<u>Para Javier</u>

<u />x = v*t\\x = 16.66*11800.83 = 196601.8 [m] = 196.6 [km]<u />

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