On a horizontal flat ground, a person is standing at a point A. At this point, he installs a 5m long pole vertically. Now, he moves 5 m towards east and then 2 m towards north and reaches at a point B. There he installs another 3 m long vertical pole. A bird flies from the top of the first pole to the top of the second pole. Find the magnitude of displacement of bird.

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Detailed Solution

From vector triangle, $\vec{A P} + \vec{P Q} = \vec{A Q}$
Hence, the displacement of the bird
$= \vec{P Q} = \vec{A Q} - \vec{A P} = 5 \hat{i} + 2 \hat{j} - 2 \hat{k}$
$P Q = \sqrt{5^{2} + 2^{2} + 2^{2}} = \sqrt{33} m$
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