A stone is dropped from the top of a cliff. The splash it makes when striking...

A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 2.5 s later. The speed of sound in air is 343 m/s. How high is the cliff?

Solutions

Expert Solution

Solution:

Let t₁ be the time taken by the rock to touch the water and.

t₂ be the time taken by the sound to reach us.

Given that t₁ + t₂ = 2.5 s    -------------(1)

Velocity of sound v = 343 m/s

Let S be the distance taveled by the rock.
          t₂ = S/v = S/343 ........... (2)
from eq. of motion, S = (1/2)g(t₁)² (initial speed u =0)
         t₂ = [(1/2)(9.8 m/s²)(t₁)²]/(343 m/s) = 0.014286(t₁)² ..........(3)
substitute the eq (3) in eq (1), we get
     0.014286(t₁)² + t₁ - 2.5 = 0
On solving the above quadratic equation we get
                      t₁ = 2.416 s

Hence distance covered by the rock is

S = (1/2)(9.8 m/s²)(2.416 s)²

S = 28.63 m

genius_generous answered 1 year ago

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