Elevator problem plz help?

Question

If an elevator moves at an acceleration of 5 ft per second squared going up and when the velocity is 8 ft/sec going up, a s***w falls from the ceiling of the elevator down to the floor of the elevator. The height of the elevator is 9 ft. Find the length the s***w dropped.

Answer 1

Suppose the s***w takes time t to reach the floor.

Take downward direction as positive.

For the s***w: -

Initial velocity u = -8 ft/s

Acceleration a = g = 32 ft/s^2

Let s1 = displacement of s***w

s1 = ut + 1/2 at^2

s1 = -8t + 1/2 * 32 * t^2

Or, s1 = -8t + 16t^2-----------------(1)

Consider the motion of the elevator. Take upward direction as positive.

Initial velocity u = 8 ft/s

Acceleration a = 5 ft/s^2

Let s2 = displacement in time t

s2 = ut + 1/2 at^2

Or, s2 = 8t +1/2 * 5 * t^2

Or, s2 = 8t + 2.5t^2---------------------(2)

s***w falls by s1 and elevator moves up by s2.

s1 + s2 = 9 ft

Therefore, from (1) and (2)

-8t + 16t^2 + 8t + 2.5t^2 = 9

Or, 18.5 t^2 = 9

Or, t^2 = 9/18.5

Or, t = sqrt(9/18.5) = 0.7 s

Using this value of t in (1)

s1 = -8 * 0.7 + 16 * 0.7^2

= 2.24 ft

Ans: 2.24 ft

Answer 2

First you have to know the missing piece:  acceleration due to gravity is downward at 32 ft/s^2.  And you have to know how to calculate the change in position given the initial velocity, acceleration, and time:

delta x = v0 t + 1/2 a t^2

In the elevator's reference frame, it falls 9 feet starting at rest with an acceleration downward of 32 + 5 = 37 ft/s^2.  From there you can calculate how long it took to fall.

In the earth's reference frame, it starts going upward at 8 ft/s and accelerates downward at 32 ft/s^2.  Fill in how long it took to fall, and you get how far it moved.

Since it started out going up, you actually don't know until you work it out whether it winds up going up or down.  I come out with it falling about 2.2 feet overall if I got my numbers right.

You can also look at how high it goes before it starts going back down.  The top is where the velocity is 0, at 8/32 = 1/4 s.  It goes up 1 foot in that time, so then it falls down 3.2 feet after that.

Answer 3

9 ft. If you are talking about compared to the elevator itself. The question could be translated to that. But, I know these questions can't be that simple. So they are asking for a comparative length within the elevator shaft. I have no idea with that one.