An elevator moves downward in a tall building at a constant speed of 4.25 m/s. E

Question

An elevator moves downward in a tall building at a constant speed of 4.25 m/s. Exactly 5.05 s after the top of the elevator car passes a bolt loosely attached to the wall of the elevator shaft, the bolt falls from rest. (a) At what time does the bolt hit the top of the still-descending elevator? (Assume the bolt is dropped at t = 0 s.) s (b) Estimate the highest floor from which the bolt can fall if the elevator reaches the ground floor before the bolt hits the top of the elevator. (Assume 1 floor 3 m.)

Explanation / Answer

According to the question

We know that

Pos_el = v0*t

Pos_el = 4.25*t + 4.25*5.05

Then,

Pos_bolt = 1/2*a*t^2 = 4.9t^2

Technically, both those functions should be negative, but whatever.

Then,

4.25t + 4.25*5.05 = 4.9t^2

t = 5.143

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