A man naming on a horizontal road at 8 `ms^(-1)` finds rain falling vertically. If he increases his speed to 12 `ms^(-1)` he finds that drops make `30^(@)` angle with the vertical. Find the velocity of main with respect to the road.

Options

A. `4sqrt(7) ms^(-1)`
B. `8sqrt(2) ms^(-1)`
C. `7sqrt(3) ms^(-1)`
D. `8 ms^(-1)`

Answer

A

Explanation

`v_(r )sin theta=v_(m)…….(1)`
`v_(r ) cos theta=v_(rm)…..(2)`
From (3)`(12-8)/(v_(rm))=1/2 therefore_(rm)=8, sin theta=(v_(m))/(v_(r ))`
`v_(m)=(4/1/sqrt(3))=4sqrt(3) v_(r )^(2)+v_(m)^(2)=8^(2)+(4sqrt(3))^(2),v_(r )^(2)=8^(2)+4^(2)xx3=4^(2)(4+3)`
`therefore v_(r )=4sqrt(7)`