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Q.

The wind is blowing from south at $10 {ms}^{- 1}$ but to a cyclist it appears blowing from the east at $10 {ms}^{- 1}$ . The velocity of cyclist is

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a

$10 \sqrt{2} {ms}^{- 1} towards S - W$

b

$10 \sqrt{2} {ms}^{- 1} towards N - E$

c

$10 \sqrt{2} {ms}^{- 1} towards N - W$

d

$10 \sqrt{2} {ms}^{- 1} towards S - E$

answer is D.

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Detailed Solution

$\vec{V_{w}} = 10 \hat{j}; \vec{V_{wc}} = - 10 \hat{i} \vec{V_{wc}} = \vec{V_{w}} - \vec{V_{c}}$
$\vec{V_{c}} = \vec{V_{w}} + 10 \vec{i}$ i, j are +ve (+i=east, +j=north)
$= 10 \hat{j} + 10 \hat{i}$
$|\vec{V_{c}}| = 10 \sqrt{2} {ms}^{- 1}$ towards N-E

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