Question on considering final velocity

[baird.lindsay]

Homework Statement

bolt comes loose underneath an elevator that is moving upward at a speed of 6.0 m/s and reaches the bottom in 3.0s . find how high above the bottom of the shaft it came loose and the speed of the bolt when it hits the bottom.

i figured out the problem but my question is why don't you consider the final velocity as 0 because when the bolt is on the bottom of the shaft there is no velocity? this is what i first tried to do when attempting to find the initial velocity but that is wrong...so i just wanted to know why i can't put v final as 0.

Homework Equations

vf=vo+at

The Attempt at a Solution

 

[Doc Al]

You are considering the motion of the bolt under the influence of gravity alone. So the 'final' velocity in your kinematic analysis should be the speed of the bolt just before it hits the floor of the elevator.

After it hits the floor of the elevator, other forces come into play.

 

[SteamKing]

Because the velocity of the bolt does not go to zero until after it has struck the bottom of the shaft.

 

[baird.lindsay]

thank you!

 

[Nickie]

In this problem, it is important to consider the final velocity because it affects the distance traveled by the bolt. The bolt is initially moving at a speed of 6.0 m/s, but as it falls, its velocity increases due to the acceleration of gravity. Therefore, the final velocity at the bottom of the shaft will not be 0. It will be greater than 0 and this affects the distance it travels.

To find the height above the bottom of the shaft where the bolt came loose, we can use the equation vf^2 = vo^2 + 2ad, where vf is the final velocity (which we have already determined is not 0), vo is the initial velocity (which we are trying to find), a is the acceleration due to gravity (9.8 m/s^2), and d is the distance traveled.

Similarly, to find the speed of the bolt when it hits the bottom, we can use the equation vf = vo + at, where vf is the final velocity (which we have already determined is not 0), vo is the initial velocity (which we are trying to find), a is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes to reach the bottom (3.0 seconds in this case).

Therefore, it is necessary to consider the final velocity in this problem because it affects the calculations for both the height and the speed of the bolt. It is incorrect to assume that the final velocity is 0, as the bolt will continue to have a velocity due to the acceleration of gravity until it hits the bottom.