I have a homework problem I'm not quite sure how to do. I tried it, and got an answer of 3.5 seconds, but am not sure if that is correct. If you could show me the answer to this question, please help. Thanks!

If you drop a stone into a mine shaft 122.5 m deep, how soon afterwards do you hear the stone hit the bottom of the shaft?

i think that your answer would be 5 seconds. Because the stone is in free fall, we use the constant acceleration equation Yf= Yi + Vi*t -(1/2) * a * t^2

which is 122.5 = 0 + 0 - (1/2) * (-9. t^2
because you choose your starting point a 0 and since your dropping the stone, it's inital velocity is 0 m/s

t= (122.5/4.9)^1/2 = (25)^1/2 = 5

That will tell you how long it takes for the stone to hit the bottom of the shaft. You then have to figure out how long it takes for the sound of the stone hitting the bottom to reach the top. time = distance/velcoity

time = 122.5/343(assuming this is the speed of sound)
time = 0.357 seconds
therefore the answer should be 5.357 seconds