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A man in a lift ascending with an upward...

A man in a lift ascending with an upward acceleration `a` throws a ball vertically upwards with a velocity `v` with respect to himself and catches it after `t_1` seconds. After wards when the lift is descending with the same acceleration `a` acting downwards the man again throws the ball vertically upwards with the same velocity with respect to him and catches it after `t_2` seconds?

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The correct Answer is:
2
Taking upward direction as positive, let us workin the frome of lift. Acceleration of ball relative to lift `=(g+a)` downwards, so `a_(real) =- (g+a)`, initial velocity: `u_(rel) =v`, final velcity : `v_(rel) =v`, as the ball will reach the man with same speed w.r.t. lift Apply `v_(rel) =u_(rel)+ a_(rel)t rArr - v+ (g-a)t rArr t =2 s` .
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Knowledge Check

  • A man in a lift throws a ball vertically upwards with a velocity v and catches it (i) after t_(1) second when the lift is ascending with an upward acceleration of 'a' and (ii) after t_(2) second when the lift is descending downward with the same acceleration 'a'. THe velocity of the ball v is

    A
    g `t_(1)t_(2)`
    B
    (1/2) g `t_(1)t_(2)`
    C
    2 g `t_(1)t_(2)//t_(1) + t_(2)`
    D
    g `t_(1)t_(2)//t_(1) + t_(2)`

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