an elevator car whose floor to ceiling distance is equal to 2.7m starts from rest with a constant acceleration of 1.2 ms^-2 . two seconds later , a bolt drops from car's ceiling.the time taken by bolt to hit floor of elevtor is..plz say..

To determine the time it takes for the bolt to hit the floor of the elevator, we need to analyze the motion of both the elevator and the bolt. Let's break this down step by step.

Understanding the Elevator's Motion

The elevator starts from rest and accelerates upwards at a constant rate of 1.2 m/s². We can calculate the position of the elevator after 2 seconds using the following kinematic equation:

• Displacement (s) = ut + (1/2)at²

Here, u is the initial velocity (0 m/s since it starts from rest), a is the acceleration (1.2 m/s²), and t is the time (2 seconds).

Plugging in the values:

• s = 0 × 2 + (1/2) × 1.2 × (2)²
• s = 0 + (0.6) × 4
• s = 2.4 m

After 2 seconds, the elevator has moved 2.4 meters upwards from its starting position.

Position of the Bolt

When the bolt drops from the ceiling of the elevator, it is at a height of 2.7 m (the total height of the elevator) minus the distance the elevator has traveled (2.4 m). Therefore, the initial height of the bolt when it drops is:

• Initial height of the bolt = 2.7 m - 2.4 m = 0.3 m

Analyzing the Bolt's Free Fall

Once the bolt is released, it is in free fall under the influence of gravity. The only force acting on it is gravity, which accelerates it downwards at approximately 9.81 m/s². We can use the following kinematic equation to find the time it takes for the bolt to hit the floor of the elevator:

• s = ut + (1/2)gt²

In this case, s is the distance the bolt falls (0.3 m), u is the initial velocity of the bolt (0 m/s, since it drops from rest), g is the acceleration due to gravity (9.81 m/s²), and t is the time in seconds.

Substituting the values into the equation:

• 0.3 = 0 × t + (1/2) × 9.81 × t²
• 0.3 = 4.905t²

Now, we can solve for t²:

• t² = 0.3 / 4.905
• t² ≈ 0.0611
• t ≈ √0.0611 ≈ 0.247 s

Total Time Calculation

The total time taken by the bolt to hit the floor of the elevator is approximately 0.247 seconds after it is released. Since the bolt drops 2 seconds after the elevator starts moving, the total time from the start of the elevator's motion until the bolt hits the floor is:

• Total time = 2 seconds + 0.247 seconds ≈ 2.247 seconds

In summary, the bolt takes about 0.247 seconds to hit the floor of the elevator after being released, and the total time from when the elevator starts moving until the bolt hits the floor is approximately 2.247 seconds.