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An elevator moves downward in a tall building at a constant speed of 4.00 m/s. E

ID: 2171992 • Letter: A

Question

An elevator moves downward in a tall building at a constant speed of 4.00 m/s. Exactly 4.95 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

An elevator moves downward in a tall building at a constant speed of 4.35 m/s. Exactly 3.55 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.

"head start" displacement top of elevator has over bolt = (5.45)(5.25) = 28.6 m at t=0.
Downward distance of elevator at any time = t:
D = 5.25t +28.6
Bolt's fallen distance (d) after t=0 at any time = t:
d = 1/2gt² = (0.5)(9.81)t² = 4.905t²
find t when D = d:
5.25t + 28.6 = 4.905t²
0 = 4.905t² - 5.25t - 28.6
solve quadratic for pos root of t:
t = 3.00s ANS (a)
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elevator distance moved downward in t = 3s
D = 5.25t + 28.6
D = 5.25(3) + 28.6 = 44.35 m
No. of floors = 44.35/3 = 14.8
Estimate of highest floor = 14th floor ANS (b)

(a) At what time does the bolt hit the top of the still-descending elevator? (Assume the bolt is dropped at t = 0 s.)

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