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A passenger in a Bus moving towards east...

A passenger in a Bus moving towards east, observes a man moving towards north. What is the actual direction of man w.r.t ground.

Text Solution

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Velocity of bus w.r.t ground `=overset(vec)V_(BG)` (east)
Velocity of man w.r.t bus `=overset(vec)u_(MB)` (North)

Velocity of man w.r.t ground `=overset(vec)V_(Mg)=?" ":.`
`overset(vec)V_(MB)=overset(vec)V_(Mg)-overset(vec)V_(Bg)" "rArr overset(vec)C_(Mg)=overset(vec)V_(MB)+overset(vec)V_(Bg)`
i.e. man is going toward North-East direction and at an angle of

`theta=tan^(-1)((|overset(vec)V_(MG)|)/(|overset(vec)V_(Bg)|))` w.r.t. east.
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