SOLUTION: Please help, I am completely stuck: A diver jumps off a diving board that is 10 ft above the water at a velocity of 12 ft/sec. His height, s , in feet, above the water can be mode

Question 1030134: Please help, I am completely stuck:
A diver jumps off a diving board that is 10 ft above the water at a velocity of 12 ft/sec. His height, s , in feet, above the water can be modeled by .
(a) How long is the diver in the air before he hits the water?
Enter the exact answer.
The diver is in the air for ____ seconds.
(b) What is the maximum height achieved and when does it occur?
Enter the exact answers.
The maximum height is ____ feet, and it occurs after ____seconds.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A diver jumps off a diving board that is 10 ft above the water at a velocity of 12 ft/sec.
His height, s , in feet, above the water can be modeled by s(t) = -16t^2 + 12t + 10.
(a) How long is the diver in the air before he hits the water?
Enter the exact answer.
When he hits the water, s(t) = 0, therefore:
-16t^2 + 12t + 10 = 0
Simplify, divide by -2
8t^2 - 6t - 5 = 0
Factors to
(4t - 5)(2t + 1) = 0
The positive solution
4t = 5
t = 5/4
t = 1.25 seconds
The diver is in the air for _1.25_ seconds.
:
(b) What is the maximum height achieved and when does it occur?
Max height occurs at the axis of symmetry x = -b/(2a)
In this equation x=t; a=-16; b=12
t =
t =
t = .375 sec to reach max height
Find the max height

s(t) = -2.25 + 4.5 + 10
s(t) = 12.25 ft
Enter the exact answers.
The maximum height is _12.25_ feet, and it occurs after _.375_seconds.
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