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 ? |
$20 ft/s^2$ $372 ft/s^2$ $215 ft/s^2$ $37.2 ft/s^2$ |
$20 ft/s^2$ |
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 $\text{ Using} : S = ut + \frac{1}{2} at^2$ $6 = 0*1 + \frac{1}{2}(32-a)*1^2$ $6 = \frac{1}{2}(32-a)$ $a = 20 ft/s^2$ |