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) (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.
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