Question

A man wearing a hat of extended length $12\text{cm}$ is running in rain falling downwards with speed $10\text{m/s}$. The maximum speed with which man can run, so that rain drops do not fall on his face (the length of his face below the extended part of the hat is $16\text{cm}$ will be :

• A. $7.5\text{m/s}$
• B. $13.33\text{m/s}$
• C. $10\text{m/s}$
• D. $12.5\text{m/s}$

Answer 1

The correct option is A $7.5\text{m/s}$

Given,

Velocity of rain with rspect to ground along $\text{x-axis}$,

$V_{R/G\left(x\right)}=0$

Velocity of rain with rspect to ground along $\text{y-axis}$.

$V_{R/G\left(y\right)}=10\text{m/s}$

Let, velocity of man$=V$


From the above figure,

$\tan \theta =\frac{16}{12}=\frac{4}{3}$

then, velocity of rain with respect to man, $V_{R/M}=V$ (opposite to man .i.e. along the negative $\text{x-}$ direction )

So, for the required condition ;

$\tan \theta =\frac{V_{R/G\left(y\right)}}{V_{R/M\left(x\right)}}$

$\Rightarrow \frac{4}{3}=\frac{10}{V}$

$\Rightarrow V=\frac{10\times 3}{4}=7.5\text{m/s}$

Hence, option (a) is correct answer.

Why this Question ? If rain drops are falling vertically with respect to ground then they will appear falling at some angle with respect to a moving observer.