A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.4 s later. if the speed of sound is 340m/s how high is the cliff?
The total time of 3.4 seconds includes the time the rock falls and the time it takes for the sound wave to return to the top of the cliff.
Where d is the height of the cliff in meters, the falling time is
=29.8‾‾‾√ t f = 2 d 9.8
... and the sound wave return time is
=340 t s = d 340
We need to set the sum of those two components to 3.4 sec and solve.
3.4=+ 3.4 = t f + t s
3.4=29.8‾‾‾√+340 3.4 = 2 d 9.8 + d 340
Not a pretty formula. I found d =51.69+ 51.69 + meters using goal seek. At that height, the rock would fall for 3.25 seconds, and the sound would return in 0.15 seconds, for a total time of 3.40 seconds.
