SOLUTION: When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 feet in t seconds. If the splash is heard 5.5 seconds later and the speed of sound is 1100 ft/sec,

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Question 123779This question is from textbook algebra and trigonometry with analiytic geometry
: When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 feet in t seconds. If the splash is heard 5.5 seconds later and the speed of sound is 1100 ft/sec, approximate the height of the cliff.
Please round the answer to the whole number. This question is from textbook algebra and trigonometry with analiytic geometry

Answer by stanbon(75887) About Me  (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^2 feet in t seconds. If the splash is heard 5.5 seconds later and the speed of sound is 1100 ft/sec, approximate the height of the cliff.
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Let the time to hit the water be "x" seconds; distance to the water =16x^2 ft
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Time sound takes to the listener is "5.5-x" seconds;
distance from spash to listener is 1100(5.5-x) = (6050-1100x) ft.
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EQUATION:
distance down distance up
16x^2 = -1100x+6050
16x^2+1100x-6050 = 0
I graphed it and found x = 5.1189
Note: You could use the quadratic formula and get the same answer.
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Height of the cliff = 16(5.1199^2) = 419.25 ft.
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Cheers,
Stan H.