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Standard XII

Physics

Relative Velocity

An elevator i...

Question

An elevator is moving up with $2.5 m s^{- 1}$ . A bolt in the elevator ceiling $3 m$ above the elevator falls. How long (in seconds) does it take for the bolt to fall on the floor of the elevator?

0.73

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0.71

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0.56

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1.06

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Solution

The correct option is C $0.56$
Initial relative velocity of bolt with respect to the elevator $u = 2.5 m / s$ from the frame of reference of the elevator.
$\Rightarrow s = u t + \frac{1}{2} a t^{2}$
$\Rightarrow 3 = 2.5 t + \frac{1}{2} 10 t^{2}$
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, $t = \frac{- 5 + 16.27}{20}$
$⟹ t = 0.56 s$

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An elevator is moving up with 2.5ms−1. A bolt in the elevator ceiling 3 m above the elevator falls. How long (in seconds) does it take for the bolt to fall on the floor of the elevator?

An elevator is moving up with $2.5 m s^{- 1}$ . A bolt in the elevator ceiling $3 m$ above the elevator falls. How long (in seconds) does it take for the bolt to fall on the floor of the elevator?