A lift is moving in upward direction with speed `20m//s` and having acceleration `5m//s^2` in downward direction. A bolt drops from the ceiling of lift at that moment. Just after the drop, the:

Options

A. velocity of bolt with respect to ground is zero.
B. velocity of bolt with respect to ground is `20m//s` in upward direction
C. acceleration of bolt with respect to ground is `5m//s^(2)`
D. none of these

Explanation

To solve the problem step by step, we need to analyze the situation of the bolt dropping from the ceiling of the lift that is moving upwards with a certain speed and acceleration.

### Step 1: Understand the motion of the lift
The lift is moving upwards with a speed of \( u = 20 \, \text{m/s} \) and has a downward acceleration of \( a = 5 \, \text{m/s}^2 \).

### Step 2: Determine the initial conditions of the bolt
When the bolt drops from the ceiling of the lift, it will have the same initial velocity as the lift at that moment. Therefore, the initial velocity of the bolt, just after it drops, is:
\[ v_{\text{bolt, initial}} = 20 \, \text{m/s} \, \text{(upward)} \]

### Step 3: Analyze the forces acting on the bolt
Once the bolt is released, it is no longer influenced by the lift's acceleration. The only force acting on it is gravity, which accelerates it downward at \( g \approx 9.8 \, \text{m/s}^2 \).

### Step 4: Determine the acceleration of the bolt
The acceleration of the bolt after it drops is:
\[ a_{\text{bolt}} = g \approx 9.8 \, \text{m/s}^2 \, \text{(downward)} \]

### Step 5: Calculate the velocity of the bolt with respect to the ground
Since the bolt has an initial upward velocity of \( 20 \, \text{m/s} \) and begins to accelerate downward at \( 9.8 \, \text{m/s}^2 \), we can analyze its motion. However, we are specifically interested in the velocity of the bolt just after it drops.

At the moment of dropping:
- The velocity of the bolt with respect to the ground is still \( 20 \, \text{m/s} \) upward.

### Conclusion
The correct answer to the question is that just after the drop, the velocity of the bolt with respect to the ground is \( 20 \, \text{m/s} \) upward.