Question

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?

Answer 1

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