Question

An elevator car whose floor-to-ceiling distance is equal to 2.7m starts ascending with a constant acceleration $1.2m/s^2;2.0s$ after the start a bolt begins falling from the ceiling of the car. Find the displacement covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

• A. 0.7 m
• B. 1.7 m
• C. 2.7 m
• D. 3.7 m

Answer 1

The correct option is A 0.7 m

Let the total time of free fall be $t$

Then at $t=2s$

$4_B=2.\frac{1}{m}/s$ $4_C=2.\frac{1}{m}/s$

$a_C=1.2m/s^2$ $a_B=-10m/s^2$

Wrt car.

distance travelled by bolt $=27m$

Then

$-2.7m=\left(4_{B/C}\right)t+a_{B/C}\left(\frac{t^2}{2}\right)$

$\Rightarrow -2.7=(2.4-2.4)t\left(\frac{-10-12}{2}\right)t^2$

$\Rightarrow 2.7=\frac{11.2}{2}{t}^2$

$\Rightarrow t^2={(\frac{2.7}{11.2}\times 2)}^{-11}=0.482s^2$

Note: $4_B=4_C$ till $t=2.3$ before the both spots to fall.

$4_B=4_C=a_{C}t=\left(1.2\right)\left(2\right)=2.4m/s$

let the displacement of the bolt be $h$ Then,

$h=4_B\left(t\right)+4_{\frac{B}{2}}{t}^2$

$h=\left(2.4\right)\sqrt{0.482}\frac{-\left(10\right)}{2}\left(0.482\right)$

$h=-0.743$

$h=\approx -0.7m$

$|h|\approx 0.7m$

Option $A$ is correct