From a lift moving upwards with a uniform acceleration a = 2 ms-2, a man throws a ball vertically upwards with a velocity v = 12 ms-1 relative to the lift. The ball comes back to the man after a time t. Find the value of t in seconds. Take g=10ms-2

Taking upward direction as positive, let us work in the frame of lift. Acceleration of ball relative to lift = (g + a) downwards, So arel = -(g + a), initial velocity: urel = v, final velocity: vrel = -v as the ball will reach the man with same speed w.r.t lift Apply vrel=urel+arelt⇒−v=v+(−g−a)t ⇒ t=2s