## Tanya kicks a ball into the air. The function that models this is f(t) = -16t^2 + 96t, where h is the height of the ball in feet and t is th

Question

Tanya kicks a ball into the air. The function that models this is f(t) = -16t^2 + 96t, where h is the height of the ball in feet and t is the time seconds

in progress 0
2 weeks 2021-09-07T22:20:46+00:00 1 Answer 0

1. The question is incomplete. The complete question is here.

Tanya kicks a ball into the air. The function that models this scenario is h(t) = -16t² + 96t, where h is the height of the ball in feet and t is the time seconds. When will the ball hit the ground?

The ball will hit the ground after 6 seconds

Step-by-step explanation:

∵ h(t) = -16t² + 96t

∵ h is the height of the ball in feet for t seconds

– That means at the ground h = 0

∵ h(t) = 0 when the ball hit the ground

0 = -16t² + 96t

Let us solve it by adding 16t² to both sides

∴ 16t² = 96t

– Subtract 96t from both sides

16t² – 96t = 0

Factorize it by taking 16t as a common factor from each term

∵ 16t² ÷ 16t = t

∵ 96t ÷ 16t = 6

16t(t – 6) = 0

Equate each factor by 0

∵ 16t = 0

– Divide both sides by 16

t = 0 ⇒ initial position

∵ t – 6 = 0

– Add 6 to both sides

t = 6 ⇒ final position

The ball will hit the ground after 6 seconds