An elevator is descending with uniform acceleration. In order to measure the acceleration, a person in the elevator drops a stone just when the elevator starts. The stone is 6 feet above the floor of the elevator when it is dropped. It is seen by the person that the stone strikes the floor of the elevator in 1 second. What can you say about the acceleration of the elevator ?
Answer & explanation
Correct answer: option 1
Acceleration of the elevator : $a$
Acceleration of the stone w.r.t. the ground : $g$
Acceleration of the stone w.t.t. the elevator : $a_{stone/elevator}$
$a_{stone/elevator} = g - a$
= $9.8 m/s^2 - a$
= $32 ft/s^2 - a \text{ ... [9.8 m/s^2 = 32 ft/s^2]} $
Displacement : s = 6 ft
Time taken : t = 1
Initial velocity : u = 0
$\text{ Using} : S = ut + \frac{1}{2} at^2$
$6 = 0*1 + \frac{1}{2}(32-a)*1^2$
$6 = \frac{1}{2}(32-a)$
$a = 20 ft/s^2$