Question
Sun April 19, 2015 By: Saptarshi Sen

A lift whose cage is 3 m high is moving up with an acceleration of 2m/s2. A piece of stone is dropped from the top of the cage of the lift when its velocity is 8m/s. if g =10m/s2 then the stone wil reach the floor of the lift after how much time?

Expert Reply
Yashvanti Jain
Mon April 20, 2015
Given that:
a = 2 m/s2, s =3m,
The lift is accelerated frame of reference and the effective downward force on the stone is (a+g).
Since, the stone is at rest with respect to the moving cage, its initial velocity is 0 
begin mathsize 12px style straight s space equals space ut squared space plus space 1 half left parenthesis at squared right parenthesis straight s equals space ut squared space plus space 1 half left parenthesis straight a plus straight g right parenthesis space straight t squared 3 space equals space 0 space plus space 1 half left parenthesis 2 plus 10 right parenthesis space straight t squared 3 space equals space 6 straight t squared rightwards arrow straight t squared space equals space 0.5 rightwards arrow straight t space equals space 0.7 space straight s end style
Thus the stone will reach the floor of the lift in 7s.
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