Question

When a man is standing, rain drops appear to him falling at ${60}^o$ from the horizontal from his front side. When he is travelling at $5km/h$ on a horizontal road they appear to him falling at ${30}^o$ from the horizontal from his front side. The actual speed of the rain is ( in $km/h$):

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is C $5$

Let the rain velocity components are $r_h$(horizontal) and $r_v$ (vertical).

$\overrightarrow{v}$ = $r_v\hat{i}+r_h\hat{j}$

Then $\frac{r_v}{r_h}$ = $\sqrt{3}$

when he is travelling at 5 km/hr, the relative velocity of rain w.r.t. man will be

${\overrightarrow{v}}_{rel}$ = $r_v\hat{i}+\left(r_h+5\right)\hat{j}$

(as the man will have to go backwards to decrease angle)

and $\frac{r_v}{r_h+5}$ = $\frac{1}{\sqrt{3}}$

These 2 equations give $r_v$ = 5$\sqrt{3}$/2 and $r_h$= 5/2. Hence total velocity $=5$