Question

A person walks at the rate of $3 \,km/hr$. Rain appears to him in vertical direction at the rate of $3\sqrt{3}\, km/hr$. Find magnitude and direction of true velocity of rain.

• A. 6 km/hr, inclined at an angle of $45^{circ}$ to the vertical towards the person’s motion.
• B. 3 km/hr, inclined at an angle of $30^{\circ}$ to the vertical towards the person’s motion.
• C. 6 km/hr, inclined at an angle of $30^{\circ}$ to the vertical towards the person’s motion.
• D. 6 km/hr, inclined at an angle of $60^{\circ}$ to the vertical towards the person’s motion.

Answer 1

Answer: (C)

$\vec{v}_{r/m} = \vec{v}_r - \vec{v}_{m}$

$\vec{v}_r = \vec{v}_{r/m} + \vec{v}_{m}$
$\tan\,\theta = \frac{3}{3\sqrt{3}} = \frac{1}{\sqrt{3}}$
$\Rightarrow \theta = 30^{\circ}$