Question

A stone is dropped into a well. The sound of the splash is heard 4.57 s later. What is the depth of the well? (Take the speed of sound to be 343 m/s.)

Answer 1

the splash is is the sum of two times: one is the time in which the stone travel from your hand to the bottom of the well, t1 and the second time is the time in which the sound come up to you, t2;
t = 4.57 s = t1 + t2
if the depth of the well is d then
d = 0.5 g t1^2
d = Vsound* t2
from here you get
0.5 g t1^2 = Vs *t2

t2 = 4.57 - t1
Vsound = 343 m/s
4.9 t1^2 = 343 (4.57 - t1)
t1 = 4.305
x = 0.5* 9.8* 4.305² = 90.81 m

t2 = t - t1 = 0.265 s

x = Vsound t2 = 343* 0.265 = 90.895 m

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