A lift is moving up with an acceleration `2m*s^(-2)` .A nail gets dislodged from the roof of the lift when its speed reaches `8m*s^(-1)` . If the height of the lift cage is 3m, find the time taken by the nail to touch the floor of the lift.

Explanation

Relative to the lift, the initial velocity of the nail is u=0 and it falls through a height of h=3 m. Inside the lift, the relative accleration due to gravity acting on the nail downwards is
`g.=g-(-a)=9.8-(-2)=11.8m*s^(-2)`
`therefore h=ut+1/2g.t^2 or, 3=0*t+1/2xx11.8xxt^2 or, t^2=(2xx3)/(11.8) or, t=sqrt(6/(11.8))=0.713s`