Question

A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of $12\text{km/h}$, he observes that the rain is falling at an angle ${60}^{\circ }$ with the vertical. The actual velocity of rain is

• A. $12\sqrt{3}\text{km/h}$
• B. $6\sqrt{3}\text{km/h}$
• C. $4\sqrt{3}\text{km/h}$
• D. $2\sqrt{3}\text{km/h}$

Answer 1

The correct option is C $4\sqrt{3}\text{km/h}$

Let $\overrightarrow{V_m}$ be the velocity of the running man.
Let the velocity of the rain be $\overrightarrow{V_r}$

From the figure, we can say $\tan {60}^{\circ }=\frac{|\overrightarrow{V_m}|}{|\overrightarrow{V_r}|}$
$\sqrt{3}=\frac{12}{|\overrightarrow{V_r}|}$
$\therefore |\overrightarrow{V_r}|=4\sqrt{3}\text{km/h}$