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. An elevator, whose floor to the ceilin...

. An elevator, whose floor to the ceiling dis tance is 2.50m, starts ascending with a con stant acceleration of 1.25 ms - 2. One second after the start, a bolt begins falling from the ceiling of elevator. The free fall time of the bolt is `[g g=10ms^(-2)`]

A

`(3)/(2)s`

B

1s

C

`(2)/(3)s`

D

`(3)/(4)s`

Text Solution

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The correct Answer is:
To solve the problem step by step, we will analyze the motion of the bolt falling from the ceiling of the ascending elevator. ### Step 1: Understand the scenario The elevator ascends with a constant acceleration of \( a = 1.25 \, \text{m/s}^2 \). The distance from the floor to the ceiling of the elevator is \( s = 2.50 \, \text{m} \). One second after the elevator starts moving, the bolt falls from the ceiling. ### Step 2: Determine the effective acceleration on the bolt When the bolt falls, it experiences two accelerations: 1. The gravitational acceleration \( g = 10 \, \text{m/s}^2 \) acting downwards. 2. The pseudo force due to the elevator's upward acceleration \( a = 1.25 \, \text{m/s}^2 \). Since the elevator is accelerating upwards, the effective acceleration acting on the bolt is: \[ a_{\text{net}} = g + a = 10 \, \text{m/s}^2 + 1.25 \, \text{m/s}^2 = 11.25 \, \text{m/s}^2 \] ### Step 3: Set up the equation of motion The bolt falls from rest (initial velocity \( u = 0 \)) and travels a distance \( s = 2.50 \, \text{m} \). We can use the second equation of motion: \[ s = ut + \frac{1}{2} a_{\text{net}} t^2 \] Substituting the known values: \[ 2.50 = 0 + \frac{1}{2} (11.25) t^2 \] This simplifies to: \[ 2.50 = \frac{11.25}{2} t^2 \] \[ 2.50 = 5.625 t^2 \] ### Step 4: Solve for \( t^2 \) Rearranging the equation gives: \[ t^2 = \frac{2.50}{5.625} \] ### Step 5: Calculate \( t^2 \) Calculating \( t^2 \): \[ t^2 = \frac{2.50 \times 1000}{5625} = \frac{2500}{5625} = \frac{4}{9} \] ### Step 6: Find \( t \) Taking the square root to find \( t \): \[ t = \sqrt{\frac{4}{9}} = \frac{2}{3} \, \text{s} \] ### Conclusion The time taken by the bolt to reach the floor of the elevator is \( \frac{2}{3} \) seconds. ---
To solve the problem step by step, we will analyze the motion of the bolt falling from the ceiling of the ascending elevator. ### Step 1: Understand the scenario The elevator ascends with a constant acceleration of \( a = 1.25 \, \text{m/s}^2 \). The distance from the floor to the ceiling of the elevator is \( s = 2.50 \, \text{m} \). One second after the elevator starts moving, the bolt falls from the ceiling. ### Step 2: Determine the effective acceleration on the bolt When the bolt falls, it experiences two accelerations: 1. The gravitational acceleration \( g = 10 \, \text{m/s}^2 \) acting downwards. ...
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