Question

Rain is falling vertically with a speed of $12\sqrt{3}m/s$. A woman rides a bicycle with a speed of $12m/s$ from East to West direction. What is the velocity of rain relative to the woman?
(Take east and vertically upward as positive x-axis and positive y-axis respectively.)

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

Answer 1

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

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 $\overrightarrow{v_R}=-12\sqrt{(}3)\hat{j}m/s$
Velocity of woman w.r.t. ground $\overrightarrow{v_w}=-12\hat{i}m/s$
Hence, velocity of rain w.r.t woman = $\overrightarrow{v_{rw}}=\overrightarrow{v_r}-\overrightarrow{v_w}=-12\sqrt{3}\hat{j}-(-12\hat{i})m/s=12\hat{i}-12\sqrt{3}\hat{j}m/s$