Question

A water balloon is dropped from a cliff. Exactly 3 sec later, the sound of the balloon hitting the ground reaches the top of the cliff. How high is the cliff? (Thanks in advance for any help you can provide!)

Answer 1

height = -4.9t^2
when t = 3
height = 4.9(9) m = appr 44.1 m

Answer 2

If you want to include the travel time of the sound, you have to look up the speed of sound in air. Let's say that is 343.2 m/s. So now, if the falling time is t, then we have

4.9t^2 = 343.2(3-t)
t = 2.88

So, the balloon fell for only 2.88 seconds, making the distance

4.9*2.88^2 = 40.64 m