A lift is moving in upward direction with speed 20 m/s and having acceleration 5 m/s2 in downward direction. A bolt drops from the ceiling of lift at that moment. Just after the drop, thea)Velocity of bolt with respect to ground is zerob)Velocity of bolt with respect to ground is 20 m/s in upward directionc)Acceleration of bolt with respect to ground is 5 m/s2d)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Velocity of Bolt with Respect to Ground is 20 m/s in Upward Direction

Given:
Initial velocity of the lift, ul = 20 m/s (upward)
Acceleration of the lift, al = -5 m/s^2 (downward)
Acceleration due to gravity, g = 9.8 m/s^2 (downward)

To find the velocity of the bolt with respect to the ground, we need to consider the motion of the bolt relative to the lift and then add the velocity of the lift with respect to the ground.

Let's analyze the motion of the bolt relative to the lift:

1. Relative acceleration:
The acceleration of the bolt relative to the lift is the difference between the acceleration due to gravity and the acceleration of the lift.
Relative acceleration, ab = g - al
ab = 9.8 m/s^2 - (-5 m/s^2)
ab = 9.8 m/s^2 + 5 m/s^2
ab = 14.8 m/s^2 (downward)

2. Relative velocity:
The relative velocity of the bolt with respect to the lift can be found using the equation:
Final velocity of the bolt relative to the lift, vb = Initial velocity of the bolt relative to the lift + Relative acceleration × Time
Since the bolt drops from rest relative to the lift, the initial velocity of the bolt relative to the lift is 0.
vb = 0 + 14.8 m/s^2 × t
vb = 14.8t m/s (downward)

Now, let's consider the velocity of the lift with respect to the ground:

The velocity of the lift with respect to the ground remains constant at 20 m/s (upward) throughout the motion.

Therefore, the velocity of the bolt with respect to the ground is the sum of the relative velocity of the bolt with respect to the lift and the velocity of the lift with respect to the ground.

Vb = Vb(lift) + Ul
Vb = 14.8t m/s (downward) + 20 m/s (upward)

Since the bolt is dropped from the ceiling of the lift, the time taken for the bolt to reach the ground is very small and can be considered as negligible. Therefore, t can be considered as 0.

Vb = 14.8 × 0 m/s (downward) + 20 m/s (upward)
Vb = 0 m/s (downward) + 20 m/s (upward)
Vb = 20 m/s (upward)

Hence, the velocity of the bolt with respect to the ground is 20 m/s in the upward direction. Therefore, option B is the correct answer.

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