Posted by Gary on .
A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff
Write an equation for the time it takes for the rock to hit water, PLUS the time for the sound of the splash to come bace. You know the total time; solve for the height, H. Use a suitable speed of sound, such as 340 m/s; you would need to assume a temperature for a more accurate value of the sound speed.
3.5 (seconds) = H/340 + sqrt (2H/g)
[3.5 - (H/340)]^2 = H/4.9
12.25 - .02059H + 8.65*10^-6 H^2
= 0.2041 H
8.65*10^-6 H^2 -0.2247H - 12.25 = 0
There will be two answers; take the positive root. Also verify my numbers.