Question

A stone is dropped into a well. The splash is heard 2.2 seconds later. What is the depth of the well to the nearest tenth of a meter?

Answer 1

Let the depth of the well be h

Given T = 2.2 s

We know T = t + t '

Where t = time taken to reach the stone from the top of the well to surface of water in the well

            = (2h/g)^1/2

         t ' = time taken to reach the sound from surface of the water in the well to top of the well

            = h / v

           = h / 340

Substittue values you get T = t + t '

                                 2.2 = (2h/g)^1/2 +(h/340)

                                      = 0.4517 + (h/340)

   2.2 = (153.57 + h )/340

                      748 = 153.57 + h

h + 153.57 -748 = 0

                            

= (-153.57 163 ) / 2

       = (-153.57 + 163 ) / 2

       = 9.45 / 2

       = 4.72

h = 4.72 x 4.72

    = 22.32 m