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

AI Thread Summary
A loose bolt drops from a ceiling in a lift that is ascending with an acceleration of 1.5 m/s² and an upward speed of 2.0 m/s. The problem requires calculating the time of flight for the bolt to reach the floor, which is 3.0 m below. The initial conditions must account for the bolt's initial upward velocity equal to that of the lift when it detaches. The equations for the motion of both the bolt and the lift need to be correctly formulated to find the solution. The correct time of flight is approximately 0.73 seconds, emphasizing the importance of considering the initial conditions accurately.
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Motion question - please help

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))

answer: 0.73sec

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...
 
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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. :)
 
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