A persons walks at the rate of 3km/hr. Rain appears to him in vertical direction at the rate of `3sqrt(3)km//hr`. Find magnitude and direction of true velocity of rain.

Options

A. `6km//hr`, inclined at an angle of `45^(@)` to the vertical towards the person's motion.
B. `3km//hr`, inclined at an angle of `30^(@)` to the vertical towards the person's motion.
C. `6km//hr`, inclined at an angle of `30^(@)` to the vertical towards the person's motion.
D. `6km//hr`, inclined at an angle of `60^(@)` to the vertical towards the person's motion.

Answer

C

Explanation

`vecv_(r//m)=vecv_(r)-vecv_(m)`

`vecv_(r)=vecv_(r//m)+vecv_(m)`
`tan theta=3/(3sqrt(3))=1/(sqrt(3)) implies theta=30^(@)`