# find the depth of the well in the following mechanics question...a very deep well is drilled vertically through the earth. when a brick is dropped into the shaft the sound of the brick hitting the...

find the depth of the well in the following mechanics question...

a very deep well is drilled vertically through the earth. when a brick is dropped into the shaft the sound of the brick hitting the bottom is heard 11.4 seconds later. taking the speed of sound to be 350 ms, find the depth of the well.

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yes first answer is wrong and i am with 2nd method

solution

distance travelled downward= distance travelled upward

distance travelled downward =s1=ut+0.5gt^2

since u=0 and g=10 and take t=t

s1=0+0.5*10t^2=5t^2

distance travelled upward=s2=350*(11.4-t)=350*11.4-350t=3990-350t

now s1=s2

5t^2=3990-350t

5t^2+350t-3990=0

solving this quadratic equation gives t=9.977772288

now s1=5t^2=5*9.977772288^2=497.78 m

I know this post is old but i think the answer given is wrong I'm trying to figure out if a stone is dropped into a well and you hear the splash 4 seconds later, how deep is the well. My professor gave us two equations one for speed how long the stone takes to go down + the speed going up. The equation is the: ((square root of d) / 4)+(d/1026). then it must be solved using the quadratic equation??