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The wind is blowing from south at 10 ms^–1, but to a cyclist it appears to be 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 – W

c

$10 \sqrt{2}$ ms^-1 towards S – E

d

$10 \sqrt{2}$ ms^-1 towards N – E

answer is D.

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Detailed Solution

${\overrightarrow V _w} = 10\overrightarrow j ;\;{\overrightarrow V _{wc}} = - 10\overrightarrow j$
${\overrightarrow V _{wc}} = {\overline V _w} - {\overline V _c} = - 10\overrightarrow i$
${\overrightarrow V _c} = {\overline V _w} + 10\overrightarrow i$ i, j are +ve (+i = east, +j = North)
$= 10\overline j + 10\overrightarrow i$
$\left| {{{\overline V }_c}} \right| = 10\sqrt 2 m{s^{ - 1}}$ towards N-E

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