Question

An elevator ascends with an upward acceleration of $2.0m{s}^{-2}$. At the instant its upward speed is $2.5m{s}^{-1}$, loose bolt is dropped from the ceiling of the elevator $3.0m$ from the floor. If $g=10m{s}^{-2}$, then

• A. the time of flight of the bolt from the ceiling to floor of the elevator is 0.11 s
• B. the displacement of the bolt during the free fall relative to the elevator shaft is 0.75 m
• C. the distance covered by the bolt during the free fall relative to the elevator shaft is 1.38 m
• D. the distance covered by the bolt during the free fall relative to the elevator shaft is 2.52 m

Answer 1

Answer: (B), (C)

Velocity of bolt relative to elevator $=2.5-2.5=0$
Acceleration of bolt relative to elevator,
$a=10-(-2)=12m{s}^{-2}\left(\because g=10m/s^2\right)$
Using the relation, $s=ut+\frac{1}{2}a{t}^2$
we have, $3.0=0\times t+\frac{1}{2}\times 12\times t^2$
or $t=\frac{1}{\sqrt{2}}s=0.707s=0.7s$
Displacement $=-2.5\times 0.71+\frac{1}{2}\times 10\times (0.71{)}^2$
$=-1.775+2.521=0.746=0.75m$
Distance covered $=2\times \frac{u^2}{2g}+$ displacement
$=2\times \frac{(2.5{)}^2}{2\times 10}+0.75$
$=0.63+0.75=1.38m$