Speed of Sound

Congratulations, you've uncovered the details of Operation: Agent Gerbil! You've left your palatial mansion and are now on your way to the Indian V.A.L.A. hide out. Your plan is to go undercover as a new recruit and take down V.A.L.A. from the inside!

On your flight to India, you suddenly realize that your calculations for determining cliff height by rock fall time are all wrong! You've forgotten to take into account the speed of sound which is 1,125 ft/sec. For example, if you dropped a 13 cm rock off a 1,125 ft cliff, your table tells you it will take 9 seconds to hit the bottom. However, it then takes another full second for the sound of it hitting the bottom to reach your ears! So the time you observe is 10 seconds!

Ignoring air resistance for now, make an equation that gives the time observed for a rock to fall, that is, the time it takes to fall plus the time it takes the sound to reach your ears (you can use t for time and x for the cliff height). Then use Wolfram Alpha to solve your equation for x which will give you the actual height of the cliff based on the observed time t. Use the equation to calculate corrected distances on your spreadsheet.