Solving a Rock Falling in a Well Problem

[mart]

Homework Statement

Well this problem consists in, as the title says. A rock fall down a well, and it took you 4 seconds to ear the noise. It would be a rather easy problem, if it didn't had the sound in consideration. Oh and rigth now I apoligize for any errors or mistakes, I'm portuguese so there are some thing that might be diferent in translation, but i was very happy to find this forum btw. Moving on:
Gravity force is not included in there you might consider 9.8m/s or 10m/s
Sound speed 360m/s
The rock fall, so no initial speed.
Consider you are with your head at the top of the well.
Don't consider air resistance

Homework Equations

average velocity
average acceleration
velocity & time
displacement & time
They are in the formulay of the forum. The problem should be able to be solved with this equaitons

The Attempt at a Solution

Well i don't have any equations to put here, because the way i tryied to solve the problem up until now was by logic. It got me to a reduntant situation where I can find the depth of the well, if i don't consider the sound, but then, considering the time that the sound took to go up that distance that i found, the well has to be smaller, but if it has to be smaller because of the sound then i have to shorten the distance that I calculated in the first place. I could do this infinite times and it would get me my solution, but unfortunally i don't know any way to do that (not needed to be infinite, but a really big number of times or so, so it would be a plausable solution). Later I though of a system. But I simply can not build it.
Im thinking the teacher would be a little bit mad if I tryed to do a computer program to do that reduntant situation 500 times... so the only way I can think of precision is the system, but I have been raping my head around it and i don't know how i can do it. Could you please help me? This is really a out of the box exercise for me I'm on 11th grade and i never seen anything like it. I have no idea how to start of build the system. To total precision i would have to consider a infinitly small amount of space and consider what was the sound gravity relation to that. But I really going blind here, even if I got to that, I don't know what to do with it, I am thinking it has something to do with the end solution. Sorry by the big text just wated to try and let out what I've thought so far. Could you please please help me.

 

[tiny-tim]

welcome to pf!

hi mart! welcome to pf!

for questions like these, give the answer a letter, and write out the formula …

in this case, call the height h, find the time to fall a distance h, and add the time for sound to travel distance h …

that should equal 4 s, and should give you a quadratic equation in √h

what do you get? ​

 

[mart]

:) I'm at

0=h+360*t1+h+5*t2*t2
4=t1+t2

I've been 1 hour stering at this trying to solve it. I just don't know what to do anymore. I'm going to keep trying for more 10 min or so i have a programing test tomorrow. But if you could give me a hint or something would be great.

I know t1 plus t2 equals t but i have t2*t2 (square, idk how to write that here). And I'm not figuring how i can solve that out

 

[tiny-tim]

hi mart!

(try using the X₂ icon just above the Reply box )

you need to find an equation for t₁ only, and another equation for t₂ only (both in terms of h) …

then use t₁ + t₂ = 4.

see you in the morning! :zzz:​

 

[mart]

like:

0=h+1/2a*t1²
and
0=h+360*t2

?

Cya tomorrow then. I really hope my teacher doesn't give the solution i wanted to arrive on it on my own. Or at least if not on my own with some help, but not with the solution in front of me :S

 

[cepheid]

Shouldn't these be

0 = h - (1/2)at₁²
0 = h - 360t₂​

?

Aside from that, what you have is good. Now, solve the first equation to get an expression for t₁. Solve the second equation for t₂. Add these two expressions together and set them equal to 4 s. Solve for h.