A Person Moves 30M North Then 20M East Than 30 Root 2 Metre Southwest His Displacement From The Origin Position Will Be?


As the movement of a person is along the y-axis

\(overrightarrow{OA} = 0hat{i} + 30hat{j} + 0hat{k} \)

As the movement of a person is along the x-axis

\(overrightarrow{AB} = 20hat{i} + 0hat{j} + 0hat{k} \)

Now by applying laws of resultant vector 45 – 45 -90 triangle property along with trigonometry

\(overrightarrow{BC} = -30sqrt{2} Cos 45 hat{i} +-30sqrt{2} Sin 45hat{j} \) \(therefore overrightarrow{BC} = -30hat{i} – 30hat{j}\)

Displacement is the change in original and final position

\(therefore overrightarrow{OC} = overrightarrow{OA} + overrightarrow{AB} + overrightarrow{AB} + overrightarrow{BC} = -10hat{i}\)

Therefore, the final displacement is – 10m in the opposite direction that is west.

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