A stone is dropped into a well The sound of the splash is he

A stone is dropped into a well. The sound of the splash is heard 6.45 s later. What is the depth of the well? (Take the speed of sound to be 343 m/s.)

Solution

The elapsed time is in two parts: the time for the stone to fall, and the time for the sound to get back to the top of the well. We know the sum of those times:

T1 + T2 = 6.45 sec.

In T1 time the stone reaches the bottom

From kinematic equation

y =uyt+(1/2)at^2

uy =0 , a =g

d = 0+(1/2)gT1^2

d =4.9 T1^2 ... (1)

In T2 time the sound from the bottom reaches us

d = vt

d =343T2 ...(3)

by solving (1) ,(2) and (3) equations we get

depth of the well is d = 173.2 m