CBSE Class 9 Answered

Let S is depth of well and the dropped stone takes t₁ seconds to reach the water surface. The we have

 

S = (1/2)×9.8×t₁² = 4.9×t₁²  ....................(1)

 

let t₂ be the time taken for the sound to reach observer. then we have

 

t₂ = S/330 ..................(2)

 

substiute for S in (2) using (1)

 

t₂ = (4.9×t₁²)/330 = 0.014 t₁² ........(3)

 

we are given t₁+t₂ = 2.5 s ...........(4)

 

using (3) in (4),  t₁ + 0.014 t₁²  = 2.5  ...(5)

by solving this quadratic equation (5) , we get t₁ = 2.418 second.

 

Hence the depth S can be obtained from (1) : S = 4.9 x (2.418)² = 28.648 m