A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 5.12 s later. If the speed of sound is 340 m/s, how high is the cliff

height of cliff (h) = 112.38m

Explanation:

The time 5.12 s is the total time it takes for the rock to fall, and for the soundwave to travel back to the top of the cliff before it is heard.

Let h be the height of the cliff in meters, the time taken for the rock to fall is given by:

Next, let us calculate the time taken fot the sound to return

now putting the values of  h from equation 2 into equation (3)

Putting the value of into equation (1)

multiplying through by 340

now let us solve the quadratic equationsss;

note, time cannot be negative, so we ignored the negative answer

putting the value of    into equation (2) to find height of cliff (h)

Therefore, height of cliff (h) = 112.38m