Problem in solving question related to acceleration and velocity

[hasnainzeenwa]

Homework Statement

s lift whose cage in 3 m high is moving up with an acceleration of 2m/s^2. A piece of stone in dropped for the top of the cage of the lift when its velocity is 8 m/s, if g = 10 m/s^2, then the stone will reach the floor of the lift after how many seconds?

Homework Equations

a = (v - u) / t
d = avg v * t

The Attempt at a Solution

I tried to think that if the lift is moving upwards, then when the stone will be dropped it won't have to fall full 3 m because the lift is also moving up so i think we have to add the velocity 8m/s and the velocity with which the stone is moving.

 

[azizlwl]

My interpretation.
http://img515.imageshack.us/img515/3747/p1010019qd.jpg

 

[harts]

You were right to think that the stone won't have to fall the full 3 meters, since the lift is accelerating upwards. But I'm not sure if that is the easiest way to think about it. Ask yourself: what is the cage/stone system's relative velocity and acceleration?