Question

A man is walking due west at the rate of $4km/h$ and the rain is falling at an angle of ${30}^{\circ }$ east of vertical with a velocity of $6km/h$. The velocity of the rain relative to the man will be

• A. $5km/h$
• B. $7.118km/h$
• C. $8.718km/h$
• D. $10km/h$

Answer 1

Answer: (C)

$8.718km/h$

$r=$rain$,g=$ground $\&m=$man
Let, the resultant $\overrightarrow{v_{rm}}$ makes an angle of $\alpha$ with east of vertical
we have, $\overrightarrow{v_{rm}}=\overrightarrow{v_{rg}}+\overrightarrow{v_{mg}}$
Horizontal component: $v_{rm}\sin \alpha =6\sin {30}^o+4=7$.........................................................$\left(1\right)$
Vertical component: $v_{rm}\cos \alpha =6\cos {30}^o=3\sqrt{3}$................................................$\left(2\right)$

Squaring and Adding $\left(1\right)\&\left(2\right),$ we get, $v_{rm}=\sqrt{49+27}=8.718km/hr$