The height h (in feet) above the water of a cliff diver is modeled by h=−16t2+8t+80 , where t is the time (in seconds). How long is the diver in the air?
Question
Answer:
The height above the water is h = -16t² + 8t + 80.When the diver is above the water, h > 0.
Solve the equation
-16t² + 8t + 80 = 0
Divide through by -8.
2t² - t - 10 = 0
Factorize.
(2t - 5)(t + 2 ) = 0
t = 2.5 or t = 2
Reject negative time, so that t = 2.5 seconds.
Therefore the time the diver is above the water is 2.5 sec.
Answer: 2.5 seconds
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