A man is standing on a road and observes that rain is failing at angle `45^(@)` with the vertical. The man starts running on the road with constant acceleration `0.5m//s^(2)`. After a certain time from the start of the motion, it appears to him that rain is still falling at angle `45^(@)` with the vertical, with speed `2sqrt(2)m//s`. Motion of the man is in the same vertical plane in which the rain is falling. Then which of the following staement(s) are true.

Options

A. it is not possible
B. Speed of the rain relative to the ground is `2m//s`
C. Speed of the man when he finds rain to be falling at angle `45^(@)` with the vertical, is `4m//s`.
D. The man has travelled a distance `16cm` on the road by the time he again finds rain to be falling at angle `45^(@)`

Explanation

`vecV_(rg)=vecV_(rm)+vecV_(mg)`
`vecV_(m)=vecV_(rg)-vecV_(mg)`
`V_(m)cos 45^(@)=V_(rg)cos 45^(@)`
`V_(m)=2sqrt(2)m//s=V_(rg)`
`V_(m)cos 45^(@)=V_(mg)-V_(rg)cos 45^(@)`
`V_(mg)=2sqrt(2)(1)/(sqrt(2))+2sqrt(2)(1)/(sqrt(2))=4m//s`
using `v^(2)=u^(2)+2` as for the motion of man.
`s=16m`.