Question

A man is travelling at $10.8{\text{km h}}^{-1}$ on a rainy day. He holds an umbrella at an angle ${37}^{\circ }$ to the vertical to protect himself from the rain which is falling vertically downwards. What is the magnitude of velocity of the rain?

• A. $3\text{m/s}$
• B. $4\text{m/s}$
• C. $7\text{m/s}$
• D. $9\text{m/s}$

Answer 1

The correct option is B $4\text{m/s}$

Let $\overrightarrow{V_r}$ be the velocity of rain and $\overrightarrow{V_m}$ be the velocity of man.
Since, $\tan \left({37}^{\circ }\right)=3/4$;
Also $\tan \left({37}^{\circ }\right)=\frac{|\overrightarrow{V_m}|}{|\overrightarrow{V_r}|}=\frac{10.8}{|\overrightarrow{V_r}|}$
∴ $\frac{3}{4}=\frac{10.8}{|\overrightarrow{V_r}|}$


$|\overrightarrow{V_r}|=\frac{4}{3}\times 10.8=14.4\times \frac{5}{18}m/s$
$|\overrightarrow{V_r}|=4m/s$