Question

Rain in falling vertically with a speed of $20m{s}^{-1}$ relative to air. A person is running in the rain with a velocity of $5m{s}^{-1}$ and wind is also blowing with a speed of $15m{s}^{-1}$ (both towards east). Find the angle with the vertical at which the person should hold his umbrella so that he may not get drenched.

• A. $ta{n}^{-1}\left(\frac{1}{2}\right)$
• B. $ta{n}^{-1}\left(2\right)$
• C. $ta{n}^{-1}\left(1\right)$
• D. $ta{n}^{-1}\left(\sqrt{2}\right)$

Answer 1

The correct option is A $ta{n}^{-1}\left(\frac{1}{2}\right)$

The velocity of the rain that is vertically falling downward is $v_r=20m/s$.
The velocity of the wind that is blowing from west to east is $v_w=15m/s$.as the person is walking $5m/s$, hence, the final velocity from west to east is $=10m/s$
Now, the resultant velocity $\overrightarrow{v}$ makes an angle $\theta$ with the vertical.
$tan\theta =\frac{v_w}{v_r}=\frac{10}{20}$ or $\theta =ta{n}^1\left(\frac{1}{2}\right)$