To a man running upwards on the hill, the rain appears to fall vertically downwards with `4 m s^-1`. The velocity vector of the man w.r.t. earth is `(2 hat i + 3 hat j) ms ^-1`. If the man starts running down the hill with the same speed, then determine the relative speed of the rain w.r.t. man.
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Options

A. (a)`sqrt(10) ms^(-1)`
B. (b)`sqrt(20) ms^(-1)`
C. (c)`sqrt(30) ms^(-1)`
D. (d)none of these

Answer

b

Explanation

Velocity of man relative to earth `overset(rarr)V_(m)//E =2 hat I + 3 hatj`
velocity of rain relative to man `overset(rarr)v_(R)//M=-4hat j`
`=2hat i-hatj -2hati-3hati=4 hat I +2 hat j |overset(rarr)v_(R //M)|=sqrt(4^(2)+2^(2))=sqrt(20) ms^(-1)`