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svlad2 [7]
3 years ago
9

Una persona camina 7 kilómetros hacia el norte, después 3 kilómetros hacia el este y, luego, 3 kilómetros hacia el sur. ¿A qué d

istancia está del punto de partida
Mathematics
1 answer:
qaws [65]3 years ago
3 0

Answer:

La persona está a 5 kilómetros con respecto al punto de partida.

Step-by-step explanation:

Considérese que la dirección norte coincide con el semieje +y y que la dirección este coincide con el semieje +x. A continuación, obtenemos las formas vectoriales equivalentes de cada afirmación:

(i) Una persona camina 7 kilómetros hacia el norte:

\vec r_{1} = 7\,\hat{j}\,[km]

(ii) Después 3 kilómetros hacia el este:

\vec r_{2} = 3\,\hat{i}\,[km]

(iii) Y luego, 3 kilómetros hacia el sur:

\vec r_{3} = -3\,\hat{j}\,[km]

El vector resultante de desplazamiento se construye a partir de la siguiente suma de vectores:

\vec R = \vec r_{1}+\vec r_{2} + \vec r_{3} (1)

\vec R = 3\,\hat{i} + 4\,\hat{j}\,[km]

Asumiendo que la distancia coincide con el desplazamiento resultante, calculamos la distancia con respecto al punto de partida mediante el Teorema de Pitágoras:

\|\vec R\| = \sqrt{3^{2}+4^{2}}

\|\vec R\| = 5\,km

La persona está a 5 kilómetros con respecto al punto de partida.

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