An elevator is moving down with $2.5 {ms}^{- 1}$ . A bolt in the elevator ceiling $3 m$ above the elevator floor gets thrown with $2.5 {ms}^{- 1}$ in the downward direction as seen from elevator frame. How long (in seconds) does it take for the bolt to fall on the floor of the elevator ?

0.4

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0.46

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0.52

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0.56

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Solution

The correct option is D 0.56
Initial relative velocity of bolt with respect to the elevator $u = 2.5 m/s$ from the frame of reference of the elevator
$\Rightarrow s = u t + \frac{1}{2} a t^{2}$
Taking downward as positive,
$\Rightarrow 3 = 2.5 t + \frac{1}{2} 10 t^{2}$
Solving the quadratic equation, $10 t^{2} + 5 t - 6 = 0$
Or $t = \frac{- 5 \pm \sqrt{5^{2} - 4 (10) (- 6)}}{2 (10)}$
Or, $t = \frac{- 5 \pm 16.27}{20}$
Taking positive sign, $t = \frac{- 5 + 16.27}{20}$
$\Rightarrow t = 0.56 s$

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An elevator is moving down with 2.5 ms−1. A bolt in the elevator ceiling 3 m above the elevator floor gets thrown with 2.5 ms−1 in the downward direction as seen from elevator frame. How long (in seconds) does it take for the bolt to fall on the floor of the elevator ?

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