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You drop a stone into a deep well and hear it hit the bottom 6.26s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about 343m/s in air. How deep is the well?

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let depth be d

and time taken bu stone to reach bottom be t1

and time taken to reach the sound from bottom to ear be t2

then distance travelled = 343*t2 = d

now t1+t2 = 6.26s

so t2 = 6.26-t1

now d= 0.5*g*t1*t1 = 343*t2 = 343*(6.26-t1)

=>4.9t1*t1 +343t1 - 2147 = 0

so t1 = 5.78 or -75.78

since time can't be negative so t1 = 5.78s

so t2 = 0.48s

hence depth,d = 343*0.48 = 164.64m

explained in details

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