A ROCK IS DROPPED INTO A DRY WELL. THE TOTAL TIME TO REACH THE BOTTOM NAD FOR THE SOUND TO TRAVEL BACK TO THE TOP IS 6.7 S. WHAT IS THE DEPTH OF THE WELL TO THE NEAREST FOOT.
Using the speed of sound = 1126 ft/s, and the old standby
s = 16t²,
the time to fall d feet is √d/4
the time for the sound to echo back is d/1126
√d/4 + d/1126 = 6.7
√d/4 = 6.7 - 0.000888d
0.0625d = 44.89 - 0.0101232d + 0.000000789d²
0.000000789d² - 0.0726232d + 44.89 = 0
d = 622 ft
622 = 16t^2
t = √622/4= 6.2 sec
622/1126 = 0.5 sec
Total: 6.7 sec