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Q.

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

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a

$10 \sqrt{2} m s^{- 1} t o w a r d s S - W$

b

$10 \sqrt{2} m s^{- 1} t o w a r d s N - W$

c

$10 \sqrt{2} m s^{- 1} t o w a r d s S - E$

d

$10 \sqrt{2} m s^{- 1} t o w a r d s N - E$

answer is D.

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Detailed Solution

$\begin{array}{l} {\vec{V}}_{w} = 10 \vec{j}; {\vec{V}}_{wc} = - 10 \vec{i} \\ {\vec{V}}_{wc} = {\bar{V}}_{w} - {\bar{V}}_{c} = - 10 \vec{i} \end{array}$
${\vec{V}}_{c} = \vec{V_{w}} + 10 \hat{i}$ [ i, j are +ve (+i = east, +j = North)]
$= 10 \bar{j} + 10 \vec{i}$
$|{\bar{V}}_{c}| = 10 \sqrt{2} {ms}^{- 1}$ towards N-E

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