Answer:
- 112 ft
- 3 - 7 seconds interval
Step-by-step explanation:
<u>Given function:</u>
- f(t) = -16t² + 96t + 112
<u>The height of the platform is the y-intercept, when t = 0:</u>
- f(0) = - 16*0 + 96*0 + 112 = 112 ft
The ball's height is decreasing once it reaches the maximum, which is at vertex.
<u>The vertex is at x = -b/2a:</u>
- t = - 96/ - 32 = 3
<u>The ball hits the ground when f(t) = 0:</u>
- - 16t² + 96t + 112 = 0
- t² - 6t - 7 = 0
- (t - 7)(t + 1) = 0
- t = 7 (positive root)
The interval is between 3 seconds and 7 seconds
