Try this problem useful for the Physics Olympiad based on Motion of an Elevator.
The Problem: Motion of an Elevator
An elevator of mass M is accelerated upwards by applying a force F. A mass m initially situated at a height
of 1m above the floor of the elevator is falling freely. It will hit the floor of the elevator after a time equal to
Discussion:
Acceleration of elevator ae= F/M ( in upward direction)
Acceleration due to gravity is in downward direction so acceleration of mass as= -g
Acceleration of mass with respect to elevator
= as-ae
=(F/M)+g
=(F+Mg)/M
We know,
s=ut+(1/2)at2
From the given problem, we have s=1m
so,
1=(F+Mg)t2/M
t=√2M/(F+Mg)
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