A man is walking on a road with a velocity 3kmhr. Suddenly rain starts falling. The velocity of rain is 10km/hr in vertically downward direction. the relative velocity of rain with respect to man is :-

Answer

`50 ms^(-1)`

Explanation

Range `(OA)=(u^(2) sin 2 theta)/(g)=(1600 xx sqrt(3))/(10 xx 2)=80 sqrt(3)`
`h = 80 sqrt(3) xx tan 60^(@) = (10 xx 80 xx 80 xx 3)/(2 xx v^(2) cos 60^(@))`
Time to strike `rArr v cos 60^(@) xx t = 80 sqrt(3)`
`rArr t =(80 sqrt(3) xx2)/(v xx1) =(10 sqrt(3))/(v)`
`h=9 sqrt(3) xx (160 sqrt(3))/(v) (480 xx 9)/(v) = (240^(2) - 38400)/(v^(2))`
`v^(2) -1600 - 18v =0`
`v =(18 pm sqrt(324)+6400)/(2)`
`rArr v =50 m//s`.