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Question 342240: 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 6 seconds later and the speed of sound is 1100 ft/sec, approximate the height of the cliff. (Give the answer to two decimal places.)
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 6 seconds later and the speed of sound is 1100 ft/sec, approximate the height of the cliff. (Give the answer to two decimal places.)
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Time for the rock to hit the water:
16t^2 = x where x is the height of the cliff.
t^2 = x/16
t = (1/4)sqrt(x) sec
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Time for the sound to travel from the water to the top of the cliff
= {6-[(1/4)sqrt(x)]} sec.
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Equation:
distance = rate*time
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distance = 1100 ft/sec*{6-[(1/4)sqrt(x)]} sec.
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distance = 6600 - (1100/4)sqrt(x)
x + 275sqrt(x) - 6600 = 0
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Solve for "x"
I graphed the equation and solve for "x":
x = 493.1403 ft.
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Cheers,
Stan H.
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