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A bird moves in such a way that it has a displacement of 12 m towards east, 5 m towards north and 9 m vertically upwards. Find the magnitude of its displacement.

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5 $\sqrt{2}$ m

5 $\sqrt{10}$ m

5 $\sqrt{5}$ m

answer is B.

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Detailed Solution

$\begin{array}{l} \bar{S} = {\bar{S}}_{1} + {\bar{S}}_{2} + {\bar{S}}_{3} \\ ∴ S = \sqrt{S_{1}^{2} + S_{2}^{2} + S_{3}^{2}} \\ = \sqrt{(12)^{2} + (5)^{2} + (9)^{2}} \\ = \sqrt{144 + 25 + 81} = \sqrt{250} = 5 \sqrt{10} m \end{array}$

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