Question

Find the displacement covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

• A. $0.7$
• B. $0.4$
• C. $0.3$
• D. $0.5$

Answer 1

The correct option is A $0.7$

Relative acceleration between the elevator car and the bolt is $a_r=a_e+a_b=a_e+g$
Relative initial velocity between the elevator car and bolt is $u_r=u-u=0$
where $u$ is the velocity of the lift when the bolt drops from the elevator car. The bolt has also the same velocity $u$ as that of the elevator car when it drops from the ceiling.
Applying the 2nd kinematics equation, $s=ut+\frac{1}{2}a{t}^2$
$S=u_{r}t+\frac{1}{2}{a}_r{t}^2=0+\frac{1}{2}{a}_r{t}^2=\frac{1}{2}\times (1.2+9.8)\times t^2$
$\therefore 2.7=\frac{1}{2}\times 11\times t^2$
$\Rightarrow t=\sqrt{\frac{1}{2}}=0.7$
At the moment the bolt loses contact with the elevator, it has acquired an upward speed of $1.2\times 2=2.4m/s$
In the reference frame attached to the elevator shaft ( ground), the distance travelled by the bolt is $2.4\times 0.7-\frac{1}{2}\times 9.8\times (0.7{)}^2=-0.7m$
Hence, distance travelled by the bolt is $0.7m$