A ship is sailing towards north at a speed of \( \sqrt{2} \mathrm{~m} / \mathrm{s} \). The curre...

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A ship is sailing towards north at a speed of \( \sqrt{2} \mathrm{~m} / \mathrm{s} \). The current is taking it towards East at the rate of \( 1 \mathrm{~m} / \mathrm{s} \) and a sailor is climbing a vertical pole on the ship at the rate of \( 1 \mathrm{~m} / \mathrm{s} \). Find the velocity of the sailor with respect to ground.
(a) \( 2 \hat{i}+\sqrt{2} \hat{j}+\hat{k} \)
(b) \( \hat{i}+\sqrt{2} \hat{j}+\hat{k} \)
(c) \( \sqrt{2} \hat{i}+\hat{j}+\hat{k} \)
(d) \( \hat{i}+\hat{j}+\sqrt{2} \hat{k} \)
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