A rain drop is falling with velocity #(2hati-4hatj)#m/s. what should be the velocity of a man so that rain drops hit him with speed 5m/s?

1 Answer
P dilip_k
Jul 8, 2017

A rain drop is falling with velocity #(2hati-4hatj)#m/s.
The velocity of the man will be in horizontal direction . So let the velocity of the man be #ahati#

So relative velocity of the rain drop w.r. to man will be # (2-a)hati-4hatj#.

By the given condition

#abs( (2-a)hati-4hatj)=5#.

#=>sqrt( (2-a)^2+4^2)=5^2#.

#=>( (2-a)^2+4^2)=25#.

#=>(2-a)^2=9#.

#=>(2-a)=pm3#.

So #a=-1 or +5#

So velocity of the man is #-hati or 5hati# m/s

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