Final answer:
The ball will take 2 seconds to hit the ground.
Step-by-step explanation:
The ball is kicked vertically into the air with an initial velocity of 32 ft/second. Given the equation h = - 16t^2 + 32t, where h is the height of the ball in feet and t is the time in seconds. We need to find how long it will take for the ball to hit the ground, which means the height is 0. To solve for t, we can set the equation equal to zero and solve for t.
0 = -16t^2 + 32t
Using the quadratic formula, t = (-b ± √(b^2 - 4ac))/(2a), where a = -16, b = 32 and c = 0. Plugging in these values, we get:
t = (-32 ± √(32^2 - 4(-16)(0)))/(2(-16))
t = (-32 ± √(1024))/(2(-16))
t = (-32 ± 32)/(2(-16))
t = -1 or t = 2
Since time cannot be negative, we discard -1 as the solution. Therefore, it will take the ball 2 seconds to hit the ground.