Question

An elevator ascends with an upward acceleration of $2.0\, ms ^{-2}$. At the instant its upward speed is $2.5\, ms ^{-1}$, loose bolt is dropped from the ceiling of the elevator $3.0\, m$ from the floor. If $g=10\, ms ^{-2}$, 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,
$a=10-(-2)=12 \,ms ^{-2} \left(\because g =10 \,m / s ^{2}\right)$
Using the relation, $s=u t+\frac{1}{2} a t^{2}$
we have, $3.0=0 \times t+\frac{1}{2} \times 12 \times t^{2}$
or $t =\frac{1}{\sqrt{2}} s =0.707 s =0.7 s$
Displacement $=-2.5 \times 0.71+\frac{1}{2} \times 10 \times(0.71)^{2} $
$=-1.775+2.521=0.746=0.75 \,m $
Distance covered $=2 \times \frac{u^{2}}{2 g }+$ displacement
$=2 \times \frac{(2.5)^{2}}{2 \times 10}+0.75 $
$=0.63+0.75=1.38 \,m$