Penny Dropped down Well Problem

[Fusilli_Jerry89]

A penny is dropped down a well. One hears the sound of it hitting the bottom 2.5 seconds later. If sounds travels at 330 m/s, how deep is the well.

What I did:
Time(penny)+Time(sound)=2.5
T(p)=2.5-T(s)
T(s)=x
T(p)=2.5-x
d=vit+1/2at^2
330x=1/2(-9.8)(2.5-x)^2
I then solved using the quadratic forumula and got -62.2 or-0.102. I then chose the 0.102 seconds and multipled it by 330 and got 33.7 m. If this is right, my question is how can both times be negative, and how can you decifer which one is right besides using common sense?

 

[OlderDan]

A penny is dropped down a well. One hears the sound of it hitting the bottom 2.5 seconds later. If sounds travels at 330 m/s, how deep is the well.

What I did:
Time(penny)+Time(sound)=2.5
T(p)=2.5-T(s)
T(s)=x
T(p)=2.5-x
d=vit+1/2at^2
330x=1/2(-9.8)(2.5-x)^2
I then solved using the quadratic forumula and got -62.2 or-0.102. I then chose the 0.102 seconds and multipled it by 330 and got 33.7 m. If this is right, my question is how can both times be negative, and how can you decifer which one is right besides using common sense?

You have sign problems? If the penny fell for the full 2.5 seconds, how far could it fall?

 

[Fusilli_Jerry89]

no the time that it fell plus the time is took for you to hear it totals 2.5 seconds.

 

[OlderDan]

no the time that it fell plus the time is took for you to hear it totals 2.5 seconds.

I know that. The point is that in 2.5 seconds the penny could not even fall as far as you said it did. You made a mistake in your calculations.

 

[Fusilli_Jerry89]

weel can you show me what i did wrong?

 

[OlderDan]

weel can you show me what i did wrong?

I don't see all your work, but it is probably here that you went wrong

330x=1/2(-9.8)(2.5-x)^2

330x is the distance the sound moves, a positive number

1/2(-9.8)(2.5-x)^2 is supposed to be the distance the penny moves, another positive number, but you made it negative. My guess is that if you get rid of the - in fornt of the 9.8 it will solve your problem.

 

[Fusilli_Jerry89]

isnt acceleration always negative tho in regards to gravity? and I thought since the penny is moving down, isn't that a negative direction?

 

[Fusilli_Jerry89]

I also did what you said and got 28.5 m which seems right. But for the time it takes the sound to reach the top, i got 0.086 sec or 72.26 sec. Why do you get two answers in this case? What is the significance of the 72.26 seconds?

 

[OlderDan]

I also did what you said and got 28.5 m which seems right. But for the time it takes the sound to reach the top, i got 0.086 sec or 72.26 sec. Why do you get two answers in this case? What is the significance of the 72.26 seconds?

This is common when you solve quadratic equations. You often get a solution that is mathematically correct, but has no physical significance.