Pot falls down toward a man: How long before we warn him?

[Const@ntine]

Homework Statement

Alright, the problem might be somewhere in the translation, or maybe I'm missing something, but anyway, here it is, word for word:

You push a pot from the edge of your balcony, which is d = 20.0 m above the ground. The pot falls towards an unsuspecting man, whose height is h = 1.75 m, and who's standing right below. Hypothesize that the man needs Δt = 0.300 s to react to any warning. How close to the ground can the pot get , so that there can be enough time for the man to react, after hearing the warning from the balcony?

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Homework Equations

V = Δx/Δt
V = 343 m/s

The Attempt at a Solution

Dunno, really. When I glansed at it, I figured it'd give me the mass, angle, initial velocities and whatnot, and it'd be a mix of an horizontal shot, and a sound wave exercise. But nope, none of that.

This doesn't specify whether it's a free fall or horizontal shot, so I guess it doesn't matter, and we're just meant to focus on the sound part of it.

Thing is, maybe it's the translation, but I'm not sure what those "0.3s" are, exactly. Is it the time it takes him to react after hearing something? That's what I thought. So I went ahead and found how much time it'd take the sound from us/me to arrive to his ears:

V = (d-h)/t_w <=> 343 m/s = (20.0-1.75) m/t_w <=> t_w = 0.0532 s

I don't have anything else though. I'm probably missing something, but time is short, so I could really use any help I can get.

Thanks a ton!

PS: This can be found in the Sound Waves chapter btw.

 

[BvU]

How long does the pot take to fall 18.25 m ? Subtract 0.3 s from that, subtract 0.0532 from that and calculate how far from the ground the pot falls in that time -- is how I read the exercise.

 

[Const@ntine]

How long does the pot take to fall 18.25 m ? Subtract 0.3 s from that, subtract 0.0532 from that and calculate how far from the ground the pot falls in that time -- is how I read the exercise.

That's what I figured when I saw the accompanying picture, but I'm not given a mass so that I may see it as a "free fall" problem. Apart from the height of the man and distance, nothing else is given. The speed of sound with the air as the means of transfer, is given as a known constant brfore the exercises.

 

[BvU]

Assume a mass (say, $m = 1$ kg). Perhaps it divides out ?

 

[haruspex]

Assume a mass (say, $m = 1$ kg). Perhaps it divides out ?

Better not to assign a value, just leave as m. If a value is plugged in it will be hard to tell whether it canceled out.

 

[Const@ntine]

I tried it again this morning and yeah, you have to do this:

-Find the time it takes for the sound to reach the man (t_s).
-Add to that the time he needs to react (t_r).
-Now you have the amount of time he needs to "evade" the pot (t_w).

-Find the time it takes for the pot to travel from the balcony to the man (t_p).
-Subtract from this time the amount it takes for him to "evade" the pot (t_u).
-Find how much distance the pot covered in that time (t_u).

He gives an answer of 7.82 m, and I got a 7.76 m, but it's probably a "significant digit" thing. I may give it another go when I'm done with this chapter, but at least I figured out how to work it. Dunno why I had it stuck in my mind that I needed to know the value of its mass. Maybe I was just tired.

Anyway, thanks everybody, I really appreciated the help!

 

[haruspex]

I tried it again this morning and yeah, you have to do this:

-Find the time it takes for the sound to reach the man (t_s).
-Add to that the time he needs to react (t_r).
-Now you have the amount of time he needs to "evade" the pot (t_w).

-Find the time it takes for the pot to travel from the balcony to the man (t_p).
-Subtract from this time the amount it takes for him to "evade" the pot (t_u).
-Find how much distance the pot covered in that time (t_u).

He gives an answer of 7.82 m, and I got a 7.76 m, but it's probably a "significant digit" thing. I may give it another go when I'm done with this chapter, but at least I figured out how to work it. Dunno why I had it stuck in my mind that I needed to know the value of its mass. Maybe I was just tired.

Anyway, thanks everybody, I really appreciated the help!

Yes, you will need to maintain a fair bit of precision to get an accurate answer. This is partly because of the quadratics, but mostly because you finish by taking a difference of two numbers of comparable magnitude.
Using g=9.8m/s²:
Time for pot to reach man = 1.930s
Time for sound = .053s.
We can allow the pot to fall for 1.577s, i.e. 12.19m, reaching a height 7.81m.

 

[Const@ntine]

Yeah, it needs a bit of attention, that's true.

PS: Sorry for the late response, I just saw it.