Question

1. **A volleyball is hit upward by a player in a game. The height h (in feet) of the volleyball after t seconds is given by g = -8t^2 + 32t +6A. After how many seconds does the volleyball hit the ground? Round to the nearest hundredth of a second.

Answer 1

The height h = -8t² + 32t +6

The ball hits the ground when height is zero, then:

-8t² + 32t +6 = 0

To solve this we will use the quadratic formula:

`t\text{ = }\frac{-(-8)\pm\sqrt[]{32^2-4(-8)(6)}}{2(-8)}=\frac{8\pm\sqrt[]{1024+192}}{-16}=\frac{8\pm\sqrt[]{1216}}{-16}=(8\pm34.8712)/(-16)`

t1 = (8 + 34.8712)/(-16) = -2.68

t2 = (8 - 34.8712)/(-16) = 1.67

Since the time cannot be negative, we choose 1.67 as the solution

Answer:

1.67 seconds