A sailor in a small sailboat encounters shifting winds . He sails 2 km east , then 4√2 km southeast , then an additional distance in an unknown direction …

Q: A sailor in a small sailboat encounters shifting winds . He sails 2 km east , then 4√2 km southeast , then an additional distance in an unknown direction . His final position is 5 km directly east of starting point . Find the magnitude of the third leg of voyage .

(a) $\sqrt{18}$ km

(b) $\sqrt{19}$ km

(c) $\sqrt{17}$ km

(d) $\sqrt{11}$ km

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Ans: (c)

Sol: $2 \hat{i} + 4\sqrt{2}cos45^o \hat{i} + 4\sqrt{2}cos45^o (-\hat{j} ) + \vec{d} = 5 \hat{i}$

$\vec{d} = 5 \hat{i} – 6 \hat{i} + 4 \hat{j}$

$\vec{d} = – \hat{i} + 4 \hat{j}$

$ |\vec{d} | = \sqrt{1^2 + 4^2 }$

$ |\vec{d} | = \sqrt{17} km$