Una persona camina 7 kilómetros hacia el norte, después 3 kilómetros hacia el este y, luego, 3 kilómetros hacia el sur. ¿A qué distancia está del punto de partida

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:

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

(ii) Después 3 kilómetros hacia el este:

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

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

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

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

[tex]\vec R = \vec r_{1}+\vec r_{2} + \vec r_{3}[/tex] (1)

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

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

[tex]\|\vec R\| = \sqrt{3^{2}+4^{2}}[/tex]

[tex]\|\vec R\| = 5\,km[/tex]

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

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