Question

A person walks at the rate of $3km/hr$. 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)

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

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