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Ludmilka [50]
2 years ago
6

Ana vive a 3 km del instituto y María en la misma carretera, 500 m. Más lejos. Todas las mañanas, a las ocho y cuarto, cogen la

bici para ir a clase. Ana pedalea a 6 m/s y María a 8 m/s. A) ¿Cuándo y dónde se encuentran? B) A que velocidad tendría que pedalear Ana como mínimo para que María no la alcanzase antes de llegar al instituto
Physics
1 answer:
timofeeve [1]2 years ago
8 0

Answer:

A) Ana y María e encuentran a las 8 hs 19 minutos 10 segundos (250 segundos después).

María y Ana  se encuentran cuando aún faltan 1500 metros para llega al instituto.

B) Ana tendría que pedalear como mínimo para que María no la alcanzase antes de llegar al instituto a una velocidad de 6.857 \frac{m}{s}.

Explanation:

A) Un movimiento es rectilíneo cuando un objeto describe una trayectoria recta, y es uniforme cuando su velocidad es constante en el tiempo. En otras palabras, el Movimiento Rectilíneo Uniforme es una trayectoria recta, su velocidad es constante y su aceleración es nula.

Para una posición inicial x0 y una velocidad v que tiene el cuerpo a lo largo del movimiento,  la posición para cualquier tiempo está dada por:

x(t)= x0 + v*t

Estableciendo el origen de referencia en el instituto, se tienen los siguientes valores:

  • x0ana= 3 km= 3000 m
  • x0maria= 3500 m

Por otro lado, Ana pedalea a 6 m/s y María a 8 m/s.

Entonces, como Ana y María se acercan al origen de referencia, la escuela, se la ecuación del movimiento para cada una de ellas es:

  • xana= 3000 - 6*t
  • xmaria= 3500 - 8*t

Ambas se encuentra cuando la posición de ellas sea la misma, esto es xana=xmaria. Entonces:

3000 -6*t= 3500 - 8*t

Resolviendo:

-6*t + 8*t= 3500 - 3000

2*t= 500

t= 500÷2

t=250 s= 4 minutos 10 segundos

<u><em>Ana y María se encuentran a las 8 hs 19 minutos 10 segundos (250 segundos después).</em></u>

Para conocer la posición en la que se encuentran debes sustituir el tiempo en la ecuación del movimiento de alguna de ellas:

xana=3000 - 6*250

xana= 1500 m

Es decir, <u><em>María y Ana  se encuentran cuando aún faltan 1500 metros para llega al instituto.</em></u>

B) Para que esto ocurra Ana y María deben llegar al instituto al mismo tiempo. Entonces, el tiempo que tarda María en llegar a al origen de referencia, la escuela, es:

0= 3500 - 8*t

Resolviendo:

3500=8*t

3500÷8= t

437.5 segundos= t

Así que, si Ana 437.5 segundos o menos, María no la alcanzaría. Siendo la velocidad la relación entre el espacio recorrido por un objeto y el tiempo empleado para ello, entonces la velocidad de Ana se calcula como:

velocidad=\frac{distancia}{tiempo}

velocidad=\frac{3000 metros}{437.5 segundos}

velocidad= 6.857 \frac{m}{s}

<u><em>Ana tendría que pedalear como mínimo para que María no la alcanzase antes de llegar al instituto a una velocidad de 6.857 </em></u>\frac{m}{s}<u><em>.</em></u>

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