Dropping Keys to find the floor you're on

[B3NR4Y]

Homework Statement

During a blackout, you are trapped in a tall building. You want to call rescuers on your cell phone, but you can't remember which floor you're on. You pry open the doors to the elevator shaft, drop your keys down the shaft, and hear them hit bottom at ground level 3.27 s later. Assume that the height of one floor is 3.0 m.

Homework Equations

$d=\vec{v}_{i} t - \frac{1}{2} g t^{2}$

(I directed my coordinate system so that down is in the negative direction.)

The Attempt at a Solution

I first write everything I know
v_i = 0 m/s (because you start at rest)
g = 9.8 m/s²
t = 3.27 s

I put this all into the equation and get the height of the building to be 52.395 m tall. Which I then divided by 3 to get the floor we're on, the 17th floor. This is wrong.

 

[Doc Al]

Note that you hear the sound of the keys hitting bottom 3.27 s later. Did you account for the time it takes sound to travel?

 

[Borek]

Assuming you found your height to be 1.4 meters above the ground level, which floor you are on?

Assuming you found your height to be 4.4 meters above the ground level, which floor you are on?

 

[nasu]

In North America you will be on the 18th floor. The 17th ends at a height of 51 m.
In some European countries they label as first floor the first above ground so you will be on the floor labeled 17, even though is is the 18th.

 

[B3NR4Y]

Doc, that's the second part of the problem haha.

 

[Doc Al]

Doc, that's the second part of the problem haha.

Part of the problem is how to translate the distance into the correct floor. That was described by others.

But accounting for the time it takes sound to travel is needed to find that distance properly.

 

[B3NR4Y]

Part of the problem is how to translate the distance into the correct floor. That was described by others.

But accounting for the time it takes sound to travel is needed to find that distance properly.

Now that I sat down after class, I put 18 in, and that's the right answer. I guess I didn't round properly or something or misunderstood what it mean. Just checking if I understand the concept now, so if it took 3.27 s for the sound to reach you, that must mean the bottom of the elevator shaft is d= 340 (m/s) * 3.27 (s) = 1111.8 m, which divided by 3 is 370.6 or 371^st floor, which while the problem states it's a very tall building I don't think it should be that tall, am I right or have I made another error?

 

[BvU]

Did the sound start its journey at the moment you let go of the keys, or at the moment they hit the ground ?

 

[B3NR4Y]

Did the sound start its journey at the moment you let go of the keys, or at the moment they hit the ground ?

The moment they hit the ground, I'd say because you'd hear the "chshsh" (or whatever sound keys make). So the order it goes is you drop the keys some height "h" -> they fall to the ground -> they hit -> make noise -> sound takes 3.27 s to travel back up to you at 340 m/s. But, alas, I'm wrong and it's probably something wrong with the way I read the problem. As that's been all my mistakes so far, not making excuses but English is my second language so some problem's wording has eluded me :(

 

[Borek]

Now that I sat down after class, I put 18 in, and that's the right answer. I guess I didn't round properly or something or misunderstood what it mean.

Please try to answer questions I posted much earlier in the thread. They were intended as a hint.

 

[B3NR4Y]

Assuming you found your height to be 1.4 meters above the ground level, which floor you are on? You are on the first floor

Assuming you found your height to be 4.4 meters above the ground level, which floor you are on? You are on the second floor.


Wow that really helped my understanding, the rounding wasn't the problem but every third meter is a floor and so any fraction of 3 above a whole number is the floor you're on. That makes more sense haha, thank you.

 

[Hatshepsut]

I shouldn't say so, but you'll get a system of 3 equations in 2 unknowns. Normally, that's overdetermined, but two of your equations will have the height alone on one side, so it becomes 2 equations in 2 unknowns. Then, solve this system.

Foregoing is just for reference, if others are looking at the conversation.

 

[Doc Al]

Now that I sat down after class, I put 18 in, and that's the right answer. I guess I didn't round properly or something or misunderstood what it mean. Just checking if I understand the concept now, so if it took 3.27 s for the sound to reach you, that must mean the bottom of the elevator shaft is d= 340 (m/s) * 3.27 (s) = 1111.8 m, which divided by 3 is 370.6 or 371^st floor, which while the problem states it's a very tall building I don't think it should be that tall, am I right or have I made another error?

No, the travel time of the sound through the air is not 3.27 s. That's the total time, after the keys are dropped.

Think of it as a two step process. At t = 0, you let go of the keys. After some time, the keys hit the floor and the noise is created. The sound travels through the air to you. At t = 3.27 the sound finally reaches your ears.

 

[B3NR4Y]

No, the travel time of the sound through the air is not 3.27 s. That's the total time, after the keys are dropped.

Think of it as a two step process. At t = 0, you let go of the keys. After some time, the keys hit the floor and the noise is created. The sound travels through the air to you. At t = 3.27 the sound finally reaches your ears.

Darn, I was thinking about the problem while driving home and came to this realization. Now it looks like I'm just copying haha, now to do the math, and hopefully get the right answer.