Question

An elevator car whose floor-to-ceiling distance is equal to 2.7 m starts ascending with constant acceleration 1.2 m/s²; 2.0 s after the start a bolt begins falling from the ceiling of the car. Find: 

(a) the bolt's free fall time; 

(b) the displacement and the distance covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

Answer 1

(a) One good way to solve the problem is to work in the elevator's frame having the observer at its bottom (Fig.).

Let us denote the separation between floor and ceiling by h= 2.7m. and the acceleration of the elevator by w =1.2 m/s²    

(b) At the moment the bolt loses contact with the elevator, it has already acquired the velocity equal to elevator given by:

Hence the bolt comes down or displaces downward relative to the point when it loses contact with the elevator by the amount 0.7 m(Fig).

Obviously, the total distance covered by the bolt during its free fall time