# Find the height and the velocity of the object

#### prishila

A bolt is detached from the lower part of an elevator cabin that is ascending with velocity 6meters/second and for 3 seconds comes to the point from where the elevator started to ascend. Find:
in which height is the end of the elevator in the moment when from it the bolt was detached. What is the velocity of the bolt when it comes to the point the elevator started to ascend.

Here's what i did:h=v0t+(gt^2)/2 vo is the first velocity
h=18+(10*9)/2=63
v^2-v0^2=2gs
v^2=2gs+vo^2=2*10*63+36 v=36
But my teacher told me that I did it wrong, because the bolt firstly goes up (maybe after it is detached from the elevator) and then goes down. Could you correct my mistake?

#### studiot

But my teacher told me that I did it wrong, because the bolt firstly goes up (maybe after it is detached from the elevator) and then goes down. Could you correct my mistake?
Yes that's right.

The bolt starts off with the same upward velocity as the elevator at the instant of detachment.

Since it is no longer being driven upwards it describes a parabola where it first rises to a max height, then falls back first to the same height as it was when it detached.

You know the acceleration, the initial velocity, the final velocity (by symmetry) and the time so you should be able to select the appropriate formula for this.

Have you drawn a diagram?

#### prishila

Should I take h=vot-gt^2/2 as they have different directions?