Question

A stone is dropped from rest into a well. The sound of the splash is heard exactly 1.60 s later. Find the depth of the well if the air temperature is 12.0°C. in m

Answer 1

We know the equation of motion,

                                           

Where, S is distance traveled by the object

             u is initial velocity of the object

              a is acceleration of the object

             t is time of motion

Let the falling time of stone is t₁ and time taken by sound to travel from the well to the ear of the person is t₂. And let the depth of the well is h. Then we can write,

                                                  

Where, g = 9.8 m/s² is acceleration due to gravity.

The speed of sound at 12^o C is 338 m/s.

therefore we can write,

                                               

According to the question,

                                            

or,                                     

Now we can write,

                                            

                                       or,

                                       or,

                                       or,

                                        or,

                                        or,

neglecting the negative value, we get

                                        

therefore,                         

therefore,                         

For any doubt please comment.