A man standing on a inclined plain observes rain is falling vertically. When he starts moving down the inclined plain with velocity `v=6m//s` observes rain hitting him horizontally.
The velocity of rain with respect to the man when he is moving down is

Options

A. `3m//s`
B. `3sqrt(3)m//s`
C. `4m//s`
D. none of these

Answer

A

Explanation

`vecv_(r,m)=vecv_r-vecv_m=vecv_r+(-vecv_m)`

`cos60^@=(|vecv_(r,m)|)/(|vecv_m|)=(|vecv_r|)/6`
`1/2=(|vecv_(r,m)|)/6implies|vecv_(r,m)|=3m//s`
`sin60^@=(|vecv_r|)/(|vecv_m|)=(vecv_r|)/6`
`implies sqrt3/2=(|v_r|)/6implies|vecv_r|=3sqrt3m//s`