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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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

We know that:

Speed = Distance/ Time

Given the speed = 350 m/s

Also, given the time = 11.4 seconds.

Then we will calculate the distance.

==> 350 = Distance / 11.4

==> Distance = 350 * 11.4 = 3990 m

Then, the depth of the well is 3990 meters.

rajput635's profile pic

rajput635 | Student, Undergraduate | eNotes Newbie

Posted on

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

spg15's profile pic

spg15 | Student, Undergraduate | eNotes Newbie

Posted on

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??

 

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