Question

An elevator ascends with an upward acceleration of 2 $m{s}^{-2}$ . At the instant its upward speed is 2.5 $m{s}^{-1}$, a loose bolt is dropped from the ceiling of the elevator 3m from the floor. ($g=10m{s}^{-2}$ ). The time of flight of the bolt from the ceiling to floor approximately is

• A. 1s
• B. 1.1s
• C. 0.7s
• D. 1.3s

Answer 1

The correct option is C 0.7s

Velocity of bolt relative to elevator = 2.5 - 2.5 = 0
Acceleration of bolt relative to elevator a = 10 - (-2) = 12 $m{s}^{-1}$
Using the relation, $s=ut+\frac{1}{2}a{t}^2,wehave3.0=0\times t+\frac{1}{2}\times 12t^2\Rightarrow t=\frac{1}{\sqrt{2}}s=0.7s$