# Relative motion in an elevator

1. Sep 3, 2010

### enderAM

1. The problem statement, all variables and given/known data
An elevator is moving upward at a constant speed of 2.50 {\rm{ m/s}}. A bolt in the elevator ceiling 3.00 {\rm m} above the elevator floor works loose and falls.

(Part C) What is the speed of the bolt according to an observer standing on one of the floor landings of the building?

(Part D) According to the observer in part C, what distance did the bolt travel between the ceiling and the floor of the elevator?

2. Relevant equations
Not sure if there really are any special equations just some kinematic equations
h = 1/2gt^2
v_y = gt

3. The attempt at a solution

I got part C correct (the question is pasted on top), which yielded an answer of 5.17 m/s. I just don't what to do for part D.

I take the velocity 5.17m/s and plug it into v_y = gt to get the time and then plug that in the equation for height (given above). I come out with 1.36 m but it doesn't look right to me. Just need someone to check my work because I don't have many attempts left for the problem (its for masteringphysics).

Last edited: Sep 3, 2010
2. Sep 3, 2010

### JaWiB

I'm not really sure what the question is asking (total distance or just displacement from starting point?) and you seem to be leaving out a detail (what time interval are we looking at? the time from when it shakes loose to when it hits the elevator floor?) but the most obvious way that I see to solve the problem is to treat the bolt as a projectile with an initial upward velocity of 2.5 m/s

That would make the equation for height h = -1/2 g*t^2 + v_0*t + h_0

3. Sep 4, 2010

### enderAM

Well in the first part of the problem (not shown) i found that the time for the bolt to fall to the floor is .782 seconds and according to an observer in the elevator the velocity would be 7.67 m/s (part 2). I don't see how an initial velocity of 2.5 m/s would fit in to this problem.

4. Sep 4, 2010

### JaWiB

To an observer outside the elevator, the bolt is traveling at 2.5 m/s upward with the elevator when it begins falling, and afterward its velocity changes by 9.8 m/s^2. The problem is no different from firing a projectile upward at 2.5 m/s

5. Sep 4, 2010

### enderAM

Thanks a lot man it helped. Such an easy problem too T.T