Question 149715: When 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 1100 ft/sec, approximate the height of the cliff.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! When 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 1100 ft/sec, approximate the height of the cliff.
:
Let t = time it takes for the rock to hit the water
then
(4-t) = time of the sound from the splash to the thrower
:
Write a distance equation; Dist = speed * time
;
Dist falling = distance sound traveled
16t^2 = 1100(4-t)
:
16t^2 = 4400 - 1100t
:
A quadratic equation:
16t^2 + 1100t - 4400 = 0
:
Simplify, divide by 4
4t^2 + 275t - 1100 = 0
:
Solve this using the quadratic formula: a=4; b=275; c=-1100
:
I got a positive solution of about 3.791 sec
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Find the dist falling (16t^2)
16(3.791^2) = 229.9 ft
:
Confirm the dist with the sound: 4 - 3.791 = .209 sec for the sound
.209 * 1100 = 229.9 ft is the cliff height
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