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Question

An elevator is moving up with an acceleration a m/s2. A person inside the lift throws the ball upwards with a velocity u m/s relative to himself. Then the time of flight of ball (in sec) will be:

A
ug+a
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B
uga
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C
2ug+a
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D
2uga
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Solution

The correct option is C 2ug+a

The scenario for motion of ball is shown w.r.t lift frame.
with respect to lift frame:
initial velocity of ball =ur=u m/s
acceleration of ball w.r.t lift: ar=(g+a) m/s2 , ve sign implies downward direction.

applying the equation of motion in lift frame:

Sr=urt+12art2 ...(i) where Sr is the displacement in the lift frame.

For t=T=Time of flight, putting Sr=0 in equation (i), we get:

0=uT12(g+a)T2

T=2ug+a seconds

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