Question

A person standing between two hills fires a gun. He hears the first echo after 1.5S and second echo after 2.5S. If the speed of sound is

332m/s, the distance between the hills is​

Answer 1

Let d be the distance of first hill , which gives an echo after 3/2s and d′ be the distance of another hill which gives echo after 5/2s , from the person .

given , speed of sound  =332m/s

now for echo from first hill ,

total distance travelled by sound =2d ,  (distance is doubled as the sound comes back to person after reflection)

total time taken  by sound =3/2s  , to travel a distance of 2d,

hence , distance=speed×time ,

            2d=332×(3/2) ,

or         d=249m ,

 for echo from another  hill ,

total distance travelled by sound =2d′ ,  (distance is doubled as the sound comes back to person after reflection)

total time taken  by sound =5/2s  , to travel a distance of 2d′,

hence , distance=speed×time ,

            2d′=332×(5/2) ,

or         d′=415m ,

therefore total distance between hills =249+415=664m .

     Third echo will be heard when sound coming to person after reflection from first hill (first echo) goes toward another hill and reflects back to person again ,

time taken by sound to reflect back to person from first hill (first echo) =3/2s ,

time taken by sound to reflect back to person from another hill =5/2s ,

therefore , total time (for third echo) =(3/2)+(5/2)=4s .

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Answer 2

distance between them 2.5-1.5=1

now s=u*t/2

1*332/2= 116