You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XIII

Physics

Relative Velocity

An elevator i...

Question

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.46

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.52

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.56

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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, $t = \frac{- 5 + 16.27}{20}$
$\Rightarrow t = 0.56 s$

Suggest Corrections

Similar questions

Q. 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 ?

Q. 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?

Q. A bolt of mass

0.2 k g

falls from the ceiling of an elevator moving down with an uniform speed of

5 m s^{- 1}

. It hits the floor of the elevator (length of the elevator

= 5 m)

and does not rebound. The amount of heat produced by the impact is (Take

g = 10 m s^{- 2})

An elevator ascends with an upward acceleration of 2 $m s^{- 2}$ . At the instant its upward speed is 2.5 $m s^{- 1}$ , a loose bolt is dropped from the ceiling of the elevator 3m from the floor. ( $g = 10 m s^{- 2}$ ). The time of flight of the bolt from the ceiling to floor approximately is

Q. An elevator without a ceiling is ascending up with an acceleration of

5 {ms}^{- 2}

. A boy on the elevator shoots a ball in vertical upward direction from a height of

2 m

above the floor of elevator. At this instant the elevator is moving up with a velocity of

10 {ms}^{- 1}

, and the floor of the elevator is at a height of

50 m

from the ground. The initial speed of the ball is

15 {ms}^{- 1}

with respect to the elevator. Consider the duration for which the ball strikes the floor of elevator in answering following questions. (

g = 10 {ms}^{- 2}

)

Join BYJU'S Learning Program

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 ?

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 ?