Answer:
To find the time it takes for the ball to reach a height of 22 feet on its upward path, you can set the height function h(t) equal to 22 and solve for t:
h(t) = 22
-16t² + 40t + 6 = 22
Now, subtract 22 from both sides:
-16t² + 40t + 6 - 22 = 0
Simplify:
-16t² + 40t - 16 = 0
Now, divide the entire equation by -8 to make it easier to work with:
2t² - 5t + 2 = 0
You can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 2, b = -5, and c = 2.
t = (-(-5) ± √((-5)² - 4 * 2 * 2)) / (2 * 2)
t = (5 ± √(25 - 16)) / 4
t = (5 ± √9) / 4
t = (5 ± 3) / 4
Now, consider both solutions:
1. t = (5 + 3) / 4 = 8 / 4 = 2 seconds
2. t = (5 - 3) / 4 = 2 / 4 = 0.5 seconds
Since you're interested in the time it takes for the ball to reach a height of 22 feet on its upward path, you should choose the positive value:
The ball reaches a height of 22 feet on its upward path after 2 seconds.
So, the correct answer is (b) 2 seconds.
Explanation: