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

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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

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36 is the final answer! : )