Question

A stone is dropped from rest into a well. The sound of the splash is heard exactly 3.00 s later. Find the depth of the well if the air temperature is 16.0°C.

Answer 1

speed of sound at Temperature T C,

v = vo + 0.6*T

= 331 + 0.6*16

= 340.6 m/s

let h is the depth of the well.

let t1 is the time taken fro the stone to hit the water.

use,

-h = voy*t - 0.5*g*t1^2

==> t1 = sqrt(2*h/g)

= sqrt(2*h/9.8) -------(2)

time taken for the sound to reach top of the well,

t2 = h/v

= h/340.6 ---(1)

total time taken

t1 + t2 = 3

sqrt(2*h/9.8) + h/340.6 = 3

==> h = 40.7 m <<<<<<<<<<<<<<<<<<<<<<<------------Answer