Question

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

• 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 $V_w=10\hat{j}$

Velocity of wind with respect to cyclist $=10\hat{i}=\overrightarrow{V_{\omega /c}}$

Let velocity of cyclist be $\overrightarrow{V_c}$

$\overrightarrow{V_{\omega /c}}=\overrightarrow{V_{\omega }}-\overrightarrow{V_c}$

$⟹\overrightarrow{V_{\omega /c}}-\overrightarrow{V_{\omega }}=\overrightarrow{V_c}$

$⟹\overrightarrow{V_c}=10\hat{j}-(-10\hat{i})=10(\hat{i}+\hat{j})$