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.

Taking upward direction as positive, let us work in the frame of lift. Acceleration of ball relative to lift = (g + a) downwards, so areal =−(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