Calculating the Velocity of an Elevator

[haruspex]

v

Can you be a bit clearer? We are now discussing the trajectory of the keys. Of the five variables I listed, acceleration, time, displacement, initial velocity and final velocity you correctly posted that we know the first three: a, t, s. Which velocity do we know?

 

[mdavies23]

Can you be a bit clearer? We are now discussing the trajectory of the keys. Of the five variables I listed, acceleration, time, displacement, initial velocity and final velocity you correctly posted that we know the first three: a, t, s. Which velocity do we know?

We know both initial=final

 

[haruspex]

We know both initial=final

Explain more. What do you think the initial speed is? How do you deduce it is the same as the final?

 

[mdavies23]

Explain more. What do you think the initial speed is? How do you deduce it is the same as the final?

The initial speed is the same as the elevator and the final speed is also the speed of the elevator

 

[jbriggs444]

If I understand where @haruspex is leading you, you can get an equation for key position above the starting point as a function of time, elevator velocity and gravity. You can get a simpler equation for elevator floor position above the starting point as a function of time, elevator velocity and gravity. You can then equate the two and solve for time.

It would seem that a simpler (but arguably equivalent) approach would be to switch for a moment to a reference frame in which the elevator is at rest. Figure out how long the keys take to drop one meter to the floor using this frame. Then switch back to the ground frame.

 

[haruspex]

The initial speed is the same as the elevator

Yes.

the final speed is also the speed of the elevator

No. This is a common blunder. The equations are for constant acceleration. As soon as the keys touch the ground the acceleration is no longer constant, so the the equations don't apply. We can only apply them up to the instant before they hit the ground, and at that time they will have quite a different velocity from the elevator's.

So we have these four: time, acceleration, initial velocity and displacement. Which SUVAT equation has those four?