Question

A man is travelling at $10.8\text{km /h}$ in a roofless car 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 velocity of the rain?
(Given: $\cos {37}^{\circ }=\frac{4}{5}$)

• 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 travelling in the car.

Given: $\cos {37}^{\circ }=\frac{4}{5}$, $v_m=10.8\text{km/h},$
$\sin {37}^{\circ }=\frac{3}{5}$
So as, $\tan {37}^{\circ }=\frac{3}{4}$ .....(i)

From fig., $\tan {37}^{\circ }=\frac{v_m}{v_r}$ ......(ii)
on comparing (i) and (ii)
$\frac{v_m}{v_r}=\frac{3}{4}$
$\frac{10.8}{v_r}=\frac{3}{4}$
$v_r=10.8\times \frac{4}{3}=14.4\text{km/h}$

Converting $\text{km/h}$ into $\text{m/s}$,
$v_r=14.4\times \frac{5}{18}$
$=4\text{m/s}$