# Calculate the time of flight of the bolt from ceiling to floor

• M3_EVO8
In summary, the acceleration of a lift with an upward acceleration of 1.5ms^(-2) is used to calculate the time of flight of a loose bolt that drops from the ceiling 3.0m above the floor. By considering the initial conditions and initial position of the bolt, the correct equations can be formed to find the time of flight, which is approximately 0.73 seconds.

## Homework Statement

A lift ascends with an upward acceleration of 1.5ms^(-2). At the instant its upward speed is 2.0ms^(-1), a loose bolt drops from the ceiling of the lift 3.0m from the floor. Calculate:
(a) the time of flight of the bolt from ceiling to floor

## Homework Equations

x(f) = x(i) + V(xi)t + (1/2)a(x)t^(2)

final position = initial position + (initial velocity x time) + (0.5 x acceleration x time^(2))

## The Attempt at a Solution

I attempted to solve this question by forming 2 equations and solving it, since when the bolt leaves the roof of the lift and by the time it reaches the floor of the lift, the lift would've moved up:

BALL: x(f) = 0.5 x (-9.8) x (t^(2))

LIFT: x(f) = 3 + 2t + (0.5 x 1.5x t^(2))

from the two above equations I could't get the right answer, so can someone please tell me if I've formed the right equations? Thanks in advance...

Look at the problem statement carefully.

Initially, until the bolt becomes free, it is traveling with the lift, and it has the same upward initial velocity as the lift at the moment it becomes free.

So rewrite BALL: x(f) = 0.5 x (-9.8) x (t^(2)) with the correct initial conditions

Also realize that the initial position of the bolt is 3 m above the inital position of the floor.

Astronuc said:
Look at the problem statement carefully.

Initially, until the bolt becomes free, it is traveling with the lift, and it has the same upward initial velocity as the lift at the moment it becomes free.

So rewrite BALL: x(f) = 0.5 x (-9.8) x (t^(2)) with the correct initial conditions

Also realize that the initial position of the bolt is 3 m above the inital position of the floor.

Thanks for your reply, I never thought of that... Thanks again. :)

## 1. How do you calculate the time of flight of the bolt?

The time of flight of a bolt from the ceiling to the floor can be calculated using the formula t = √(2h/g), where t is the time of flight, h is the height of the ceiling, and g is the acceleration due to gravity (approximately 9.8 m/s²).

## 2. What is the value of g in the equation?

The value of g in the equation is the acceleration due to gravity, which is a constant value of approximately 9.8 m/s² on Earth.

## 3. How do you measure the height of the ceiling for the calculation?

The height of the ceiling can be measured using a measuring tape or ruler. Simply measure the vertical distance from the floor to the ceiling to get the value for h in the equation.

## 4. Can this equation be used for objects other than bolts?

Yes, this equation can be used for any object that is dropped or thrown from a given height on Earth. However, it may not be accurate for objects that are affected by air resistance or objects on different planets with different values for g.

## 5. Is the calculated time of flight affected by the mass of the bolt?

No, the mass of the bolt does not affect the time of flight. The equation only takes into account the height and acceleration due to gravity, not the mass of the object.