How to solve Motion Question?

A lift ascends with an upward acceleration of #1.25ms^-2#. At the instant its upward speed is #2.50ms^-1#, a loose bolt falls from the ceiling of the lift, #2ยท75m# from the floor.

Calculate:
(a) the time of flight of the bolt from the ceiling to the floor
(b) the distance it has fallen relative to the lift shaft.

1 Answer
Jane
Feb 5, 2018

When the bolt was moving along with the lift,it had the same velocity and acceleration to that of the lift.

The moment it was dropped,it had an upward velocity of #2.50 m/s# and downward acceleration of #(g+1.25) m/s^2 = 11.75 m/s^2# (thinking from non inertial frame of reference,as required)

Suppose, it took #t# time to fall to the floor from the ceiling.

So,we can write, #2.75 = 1/2 11.75 t^2# (using #s=ut +1/2at^2# and taking downward direction to be positive)

Solving we get, #t= 0.68 s#

In that time,lf the bolt has gone downwards by a distance of #s# w.r.t the liver shaft, then, #s=-2.50 *0.68 + 1/2 *10 (0.68)^2 m = 0.612 m# (as we have taken upward direction negative)

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