Question

1. a metro train starts from a terminal station the train heads north for 475 m, then west for 165 m, then north for 410 m, then east for 650 m where it arrives at the next station what is the magnitude of the displacement vector from the terminal station to the next station? 1460 m 1010 m 1700 m 1220 m

Explanation:

Step1: Calculate the net displacement in the north - south direction

The train moves north twice. The total displacement in the north direction \(y=(475 + 410)\text{ m}=885\text{ m}\) (since north - south is one axis and we assume north as positive).

Step2: Calculate the net displacement in the east - west direction

The train moves west (\(x_1=- 165\text{ m}\)) and east (\(x_2 = 650\text{ m}\)). The net displacement in the east - west direction \(x=(650-165)\text{ m}=485\text{ m}\) (assuming east as positive).

Step3: Use the Pythagorean theorem to find the magnitude of the displacement vector

The magnitude of the displacement vector \(d=\sqrt{x^{2}+y^{2}}\). Substitute \(x = 485\text{ m}\) and \(y = 885\text{ m}\) into the formula:

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Answer:

1010 m