Question

Wind is blowing from the south at $10{\text{ms}}^{-1}$ but to a cyclist it appears to be blowing from the east at $10{\text{ms}}^{-1}$. The cyclist has avelocity

• A. $10\hat{i}-10\hat{j}$
• B. $10\hat{i}+10\hat{j}$
• C. $-10\hat{i}+10\hat{j}$
• D. $-10\hat{i}-10\hat{j}$

Answer 1

The correct option is B $10\hat{i}+10\hat{j}$

Velocity of wind is $10{\text{ms}}^{-1}$ from south to north i.e
${\overrightarrow{v}}_{wind}=10\hat{j}$

But to the cyclist it appears to blow from the East at $10{\text{ms}}^{-1}$. So, velocity of wind relative to the cyclist is $10{\text{ms}}^{-1}$ from the east to west. i.e
${\overrightarrow{v}}_{wind/cyclist}=-10\hat{i}$
since ${\overrightarrow{v}}_{wind/cyclist}={\overrightarrow{v}}_{wind}-{\overrightarrow{v}}_{cyclist}$
$\Rightarrow -10\hat{i}=10\hat{j}-{\overrightarrow{v}}_{cyclist}$
$\Rightarrow {\overrightarrow{v}}_{cyclist}=10\hat{i}+10\hat{j}$
Hence, the correct answer is (B).