IF A ROCK IS DROPPED FROM A CLIFF INTO AN OCEAN IT TRAVELS A

IF A ROCK IS DROPPED FROM A CLIFF INTO AN OCEAN, IT TRAVELS APPROXIMATELY 16t SQUARED FEET IN t SECONDS. IF THE SPLASH IS HEARD 4 SECONDS LATER AND THE SPEED OF SOUND IS 1,100 FT/SEC, APPROXIMATE THE HEIGHT OF THE CLIFF.

Solution

We know that the distance the rock falls = distance the sound travels
:
Let the time the rock fall = t; time the sound travels = (4-t)
:
Rock dist = sound dist
16t^2 = 1100(4-t)
16t^2 = 4400 - 1100t
16t^2 + 1100t - 4400 = 0
:
Simplify divide by 4
4t^2 + 275t - 1100 = 0
:
Using the quadratic formula (and a good calculator) the positive solution:
t = 3.79096 seconds for the rock to fall
:
Distance = 16 * 3.79096^2 = 229.94 ft
:
Check the distance with the sound: 1100(4-3.79096) = 229.94 ft also