Question

Rain is falling vertically with a speed of $12\sqrt{3}\text{m/s}$. A woman rides a bicycle with a speed of $12\text{m/s}$ in East to West direction. What is the velocity of rain relative to the woman? ( <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Eastward and upward are positive x-axis and y-axis respectively)

• A. $(12\sqrt{3}\hat{i}+12\hat{j})\text{m/s}$
• B. $(12\sqrt{3}\hat{i}+12\sqrt{3}\hat{j})\text{m/s}$
• C. $(12\hat{i}+12\sqrt{3}\hat{j})\text{m/s}$
• D. $(12\hat{i}-12\sqrt{3}\hat{j})\text{m/s}$

Answer 1

The correct option is D $(12\hat{i}-12\sqrt{3}\hat{j})\text{m/s}$


Let West to East direction be positive x – axis and upward direction be positive y – axis.
Therefore,
Velocity of rain fall w.r.t ground ${\overrightarrow{v}}_R=-12\sqrt{3}\hat{j}\text{m/s}$
Velocity of bicycle w.r.t. ground ${\overrightarrow{v}}_W=-12\hat{i}\text{m/s}$
So, velocity of rain w.r.t bicycle, ${\overrightarrow{v}}_{RW}={\overrightarrow{v}}_R-{\overrightarrow{v}}_W=-12\sqrt{3}\hat{j}-(-12\hat{i})=(12\hat{i}-12\sqrt{3}\hat{j})\text{m/s}$