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A man standing still finds rain pouring ...

A man standing still finds rain pouring at angle `30^(@)` with vertical , when he starts walking forward at a speed of 4Kmph it appears to him that rain pours vertically down. When he runs at triple the speed, what is the angle at which rain appers to pour ?

Text Solution

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Case (i) : When the man is still
`V_(R)`=actual (absolute )
velocity of rain.

Case (ii) : When man walk at 4kph,
rain falls vertically
means horizontal component of
rain.s velocity=4
`:.V_(R)sin 30^(@)=4rArr V_(R)=8`

Case (iii) : The man runs at triple the speed `V_(M)=12kph`
We have superimposed `-V_(M)"to " V_(R)`to
get the resultant.
from figure , we see `tanphi=(O.B)/(OO)=(12-4)/sqrt(8^(2)-4^(2))=8/sqrt(48)=2/sqrt3 :. phi=49`
and raindrop makes an angle of `49.6^(@)` in opposite direction .
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